What's so great about blackboards? Many mathematicians seem to think that the only way to give a mathematics talk is by using chalk on a blackboard.  To some, even using a whiteboard is heresy.  And we Don't Talk About Computers.
I'd like to know people's opinions on this.  In a - probably useless - attempt to forestall a flame war, let me try to narrow down the question a little.


*

*I'm interested primarily in the effect that the medium has on the talk.  This will make comparisons difficult since saying "X gave a rubbish talk using a computer" leaves open the possibility that X would have given an even worse talk using a blackboard.  So please try to analyse why you have a preferred medium for presentations.  This isn't meant to be a collection of tips for making good presentations (though I can see the value in that).

*It may be just my impression, but it seems that this attitude is peculiar to mathematicians.  Is this true, in your opinion?  Is there something special about mathematics that makes it so right for blackboard talks?

*I'm interested in opinions both as speakers and listeners.  Your answers are allowed to be different from the different perspectives!

*It may be that the type of talk has a bearing on the medium.  Try to take this into account as well.

*I'm possibly completely out of date on this - maybe everyone has now fully Embraced Their Inner Beamer.

*Please be nice.  By all means, praise good behaviour ("X gave a really nice talk using a combination of rope, blancmange, and a small aubergine; it wouldn't have worked so well with only chalk") but let bad behaviour rot in the dungeon of obscurity.
 A: In my experience, "messy" blackboard lectures can mostly been blamed on lack of preparation. Using beamer forces you to prepare your lecture in advance, but I think that a well prepared lecture on a blackboard is easier to digest. Some reasons for this are:


*

*Since one has to write everything down, the natural tendency is to make short, concise statements.

*Things stay on display for longer periods.

*If there is a mistake, you just erase and correct it, this is harder to do with a beamer talk (unless you have an electronic board or a tablet).

*The writing pace ensures not to rush over concepts that one finds trivial or boring. Very important when teaching freshmen (or any undergrads).


When writing a beamer presentation (usually do that for short talks in conferences) it is easy to write too much or too little on a slide, I personally find very hard to find a good balance.
This is no defense of a "blackboard ONLY" setup, though, my ideal framework is giving most of the lecture in a blackboard whilst having an auxiliary beamer to display graph plots, animations, and other additional material. Main part of the lecture goes to the board, nonetheless.
As for Blackboard vs whiteboard that is a matter of taste. I prefer the blackboard because tend to get my hands very dirty with markers and the more consistent contrast, as opposed to struggling to find the marker that isn't almost empty, often resulting in odd color combinations, but I agree that could be solved by carrying my own set of markers :-)
A: I prefer blackboards/whiteboards to any other option (even OHP) for the following two reasons:
1) I find nowadays (having been giving talks for about 15 years) that I only semi-prepare them now, and never use notes, and just say what comes out: I have a "plan" and talk around it. This way I'm guaranteed to never give the same talk twice, which is interesting for me and interesting for the audience.
2) Can't be bothered to make slides!
A: As a speaker, I have to say that a lot of my preference for blackboards over whiteboards (and, to a lesser degree, computers) is aesthetic.  I have always sort of rolled my eyes at writers waxing on about the physical feeling of a pen in their hand, or the force required to press the keys of a typewriter as opposed to those on a computer, but perhaps I should take it easy on them, because I have similar feelings about chalk.
A: The fact that giving a presentation at the black board slows down the speed of presentation and helps the audience to digest the stuff is related to the fact that mathematicians use a language that has a high information density (formulas, diagrams) compared to other fields. Moreover the symbols and other structures used in that language CAN be written on a black board. This is different for a biologist say: using a black board for him/her can be very inefficient, because of the necessity to write down more or less complete sentences or long phrases. This is too much of slowing down. Information dense structures used in biology are pictures or visualizations of numerical data that are hard to create at the black board.
A: For me it depends on the type of talk. But if I'm giving either a lecture or a seminar that involves presenting proofs (or sketches of proofs) then I like blackboards best. There are many reasons for this, but three important ones are (i) it forces me to understand the material well enough to memorize it (I don't use notes for talks, and what I say applies much less to a blackboard talk where the speaker copies from a sheaf of notes) and do the necessary calculations in real time, (ii) it slows the presentation down and gives the audience a chance to digest it, and (iii) what I write lasts for much longer before being erased.
Of these factors, I think the most important is (i): it makes giving the talk a dynamic process that cannot be done on autopilot. I wouldn't say that this cannot be achieved in other ways, and I do give Beamer talks sometimes (but only when they are very non-technical), but ultimately I'm a blackboard person. I have nothing rational against whiteboards, but I like them much less ...
A: When you write something on the blackboard, you have to think and verify that what you are writing is correct. A good speaker shares this chain of thought with the audience.
At every pause where the speaker has to think, the (good) audience will automatically try to understand what the problem could be.
An example would be in what order one might want to integrate. A pause where the speaker thinks, hints that this is a place where one easily makes mistakes, and this knowledge is passed to the audience. A Beamer presentation will most likely just display the integrals in the right order, and hence the audience does not get the chance to "feel" how one should think when integrating over multiple variables.
Beamer presentations are in some sense too well prepared to give the feeling of how one should think; imagine watching a film on the cinema but you display the solution to the problem before the actors really face them.
So, part of the presentation is to see the speaker be presented a problem, and experience how she/he tackles it. And that is why Blackboards > Beamer.
A: My only issue with whiteboards is that many people don't know how to use whiteboard pens; I've seen many professional mathematicians take off the lid, write a sentence, then talk with the lid still off. A whiteboard marker should last a very long time; certainly throughout a full talk with only the one marker.
On those grounds, I prefer blackboards. But if everyone recapped the lid automatically the moment they were done writing, even if just for a few moments... then I wouldn't really care that much.
A: Some of the best seminar presentations I have seen have been blackboard based. But personally, I really like to be able to have both a blackboard and a video projector. I can use the projector for highlights, theorem statements, pictures that are too hard or time consuming to draw by hand. But for sketching out an argument or giving a detailed proof, the blackboard shines, for much the same reasons as outlined in other answers. Unfortunately, one can rarely rely on being able to do both at the same time, but I would like that to change.
A: A major reason for giving live talks is that you can react to the audience and adjust your talk. This is difficult with slides. Even experienced speakers overestimate how much information they can convey in a lecture and are stuck with flashing through slides that almost no one is understanding. I have heard good talks using slides, but they are rare.
On some anniversary BBC.com asked readers for their view on PowerPoint. According to the responses no one had ever heard a good PowerPoint talk.
My advice is to never use slides/beamer when a blackboard available.
Paul Halmos once wrote: even a good expository paper, read out loud, would make an awful lecture --- but no worse than some I have heard.
Too many beamer talks are expository papers read out loud. 
A: Depends on


*

*Type of talk

*Room

*Audience size

*Knowledge about audience's knowledge

*Amount of content vs allotted time


(1) has been commented on already. For (2), I mean that some rooms do not have stadium seating or sliding blackboards, and the chalkboard can only be seen by the first two or three rows. Some rooms are so large that the blackboard becomes un-useful. The size of the room interacts with (3), but there's another point here. A large audience will let you say what you thought you were going to, but a small audience is much more likely to get involved with some tangent or detail, and benefit from flexibility. Sometimes, I go to give a talk and I'm not really sure who the audience will be. Using a blackboard allows for minor (and major) changes, like replacing a generic finite field with "integers mod p", or including some more easy examples, or an example of a more general nature. (5) is self explanatory.
One more comment for (1): sometimes a nice graphic (perhaps interactive, using Mathematica's Manipulate) provides a tremendous amount of clarity. And sometimes just having eye candy is nice.
A: Many excellent points are made in the above responses.  I suggest another point of view that may be important. It might be that at some point you will work in industry.  I've found that PowerPoint is often the preferred mode of presentation.  It is useful for everyone to learn how to use this medium if only because it may facilitate working with certain groups - industry.
For myself, I like the flexibility and simplicity of a blackboard.
Suggestion for whiteboard users - if you find a "dry" pen, throw it away!  All to often, I see someone discover that a pen doesn't write, put the cap back on, and return it to the tray.  Tossing it out would be helpful.
Final comments: 
Edward R Tufte 
Dr. Tufte, in my opinion, dislikes any PowerPoint presentation. The information desensity is just too restricted.  See his web site www.edwardtufte.com/tufte
Gapminder
There are some amazing examples of what can be done with a flexible electronic media in presentating data. See www.gapminder.org
A: First of all, I completely agree with Tim Gowers' first sentence.  However, I put the dividing line between presentations and board-talks much further over towards presentations than everyone else.
As a speaker:


*

*Giving a beamer talk means that I have to prepare the talk properly.  I have to think about the audience that I am speaking to, the level at which I want to present the material, and exactly what I want to say about it.  At a finer level, I have to think at each stage "What can the audience see at this point?  Am I asking them to remember something that they can no longer see, and that is no longer at the forefront of their minds?".

*Giving a presentation means that I can focus more on content.  This may seem a strange one, but in a board talk I always have to think about how much I can physically write on the board.  This may seem like I am advocating the use of beamer to stuff more stuff on to each slide but I'm not.  What I'm saying is that the amount of chalk/pixels used should not be a major factor in deciding what to put in or leave out of a talk.

*Giving a presentation means that I can focus more on the audience.  I'm constantly having to think "what can they see?" "how long ago did I say that?  Will they still remember?" "what are they going to remember from this talk?"

*Giving a presentation means that I can vary the style according to what is appropriate.  I can use colour if I think it helps, I can add complicated pictures - even animations - without difficulty.

*Giving a presentation keeps me focussed on the talk that I planned to give, not on the talk that X wants to hear.  The problem is that X is only one person in the audience.  I know what I can talk about, I've published an abstract so everyone else knows what I intend talking about, deviating from this should only be done with extreme reluctance.

*Giving a presentation means that I'm always facing the audience.  I only need to turn my head a fraction to be able to see the slide to check that it's the right one.  If I use a decent computer then I don't even need to do that.  So I can gauge the reactions in real time as the audience reads and listens.

*Giving a presentation means that I don't have to worry about how fast the audience can write.  I can make a handout available ahead of time that they can print out and bring along.  Then they can make the odd note if they need to, but the majority of the talk is already in front of them.  This is particularly useful in multi-lingual situations, as I've been finding out.

*A word about technology.  Using a graphics tablet (not even a tablet PC) more than makes up for the lack of so-called "interactivity".  It's not hard to get used to it, the range of what you can do is larger, the fact that it is different to the main presentation reminds me that what I'm doing is not the main presentation (so get back to it as soon as possible!), and it's easy to save the resulting pictures so that the audience can get hold of them later if they want.

*And a presentation can have short-cuts (one colleague advocates putting in "skip proof" links even if you haven't included a proof - the audience will think that you are skipping a proof to get to the interesting stuff and will react favourably!), and extras, and the like.  Being a presentation, though, I am forced to think about these in advance which means that I will actually have something sensible to say.
Of course, a good speaker will do all of this (even the animations!) for a board talk.  I have found that for me, I do this naturally for a presentation, but I don't for a board talk.
As a listener, here's why I prefer a presentation to a board-talk:


*

*I can concentrate on the content, not on copying it down.  I write down what's said so that if I miss something then I can look it up later, but having to concentrate on copying it down guarantees that I will miss something.  This, for me, is the Big One.

*It's a lot harder to derail a presentation.  If the talk was meant to be on "elliptic cohomology" then I want to hear about elliptic cohomology, and not about symplectic 4-folds.

*There's more variety.

*Presentations are often lighter than board-talks.  I'm afraid that for a high percentage of the talks that I go to, I really am just going to remember one thing.  So wading through heavy details is going to go in one ear and out the other.  Even if the talk is in exactly my area then what I really want to know is a reason to read the related paper, not all the details of said paper.  So a lighter talk is going to mean that I'm still paying attention at the end, rather than just mindlessly copying from board to pad.
So, in summary, doing a presentation means that I give a better talk.  Hearing a presentation means that I get more out of it.  That's why I'm broadly in favour of presentations.
A: I agree with the comments from gowers, javier etc. on why blackboards are preferable to PowerPoint and similar media, but I thought that I might try to cover in a little more depth why mathematicians might prefer them specifically to whiteboards: (i) material written on a blackboard is more easily visible, especially at long ranges, and especially compared to text written with a whiteboard pen which is part-way through its lifespan and no longer writes boldly; (ii) chalk is more reliable than a pen: a quick glance at a stick of chalk will tell you how much more you can write with it, but a whiteboard pen can fail at any time, and in my experience too often does; (iii) as they age, whiteboards can acquire a grey patina of accumulated ink which won't wash off; (iv) in my experience at least, whiteboards often just tend to be smaller.
A: Here is an answer from the viewpoint of an adviser of graduate students.  A graduate student can give a talk on Beemer without actually understanding what they are saying.  It is impossible to give a decent blackboard talk without so understanding.  I am coming around to the position that all graduate student talks (thesis defenses, but we also have a sort of oral exam that is part of the prelim that involves giving a talk) should be blackboard only.  (To give credit where it is due, this idea is due to my colleage Billy Chan). 
A: While good math presentations are spectacular, they are very hard to produce. On the the other hand, it is very easy to produce very bad ones.
