What counts as an 'invited' talk? When you write your CV, what do you count as an invited talk? Does it count if you're invited but not provided funding (this has happened to me several times at AMS special sessions)? What if someone runs into you in the hallway and invites you, but never sends you a 'formal' invitation email? What if you're a PhD student and your advisor asks you to give a talk in the department seminar or in a conference they are organizing?
Also, does it even matter? What if I just put a section in my CV called "talks" and not worry about the distinction?
Thanks in advance!
 A: What you might want to put on the CV will  depend strongly on what you are trying to accomplish with the CV.  If the CV is going to be used for job applications, then a simple list of talks given may be adequate, encompassing all of the categories listed above and others.
If the CV is going to be used for internal promotion and a tenure committee, then breaking it down by level of talk (seminar series in your own department, colloquium, conference, international symposium, etc.) may be more important.  If so, it would also be smart to emphasize collaborative efforts, such as being invited to give talks at different universities in your own department, mathematics, or being invited by different departments at your own institution or other institutions which may lead to collaborative research, such as speaking in an engineering department or the computer science department.
If your CV is being used for job hunting purposes, you may also not want to list too many talks at different universities.  This is a tricky point.  A certain number of job talks (presentations given as part of a job interview) may make you look like a more promising candidate to be hired.  Too many obvious job talks over too many years may just look like someone who has been able to pass the first level of review and look inviting enough to invite for a thorough look, but not inviting enough to tender a job offer.  But that's a subjective fuzzy threshold: how many are too many job talks?

I've given quite a few talks and been invited in various ways:


*

*the hallway invitation request to talk at a departmental seminar

*the e-mail request to give a talk on a particular topic which I'm well known to be interested in and working in

*the invitation to visit an out-of-town university and research center to talk about my work in the hopes of a possible collaborative research offer

*twice I have been asked to be part of a conference as an invited speaker, for which there were the formal trappings of being on a printed 4-color foldout brochure and part of the conference proceedings and abstracts, etc., being picked up at the airport and dining with the big-wigs and organizers of the conference and such, in which I received invitations to be a presenter by e-mail

*an invitation by a group (sub-department, which used to be its own department but became melded into or subsumed into another department) to give a talk about the application of their field in my line of work (and this group actually wined-and-dined me as if I were a job candidate, including schmoozing with higher level dean type people at the pre-talk luncheon...)
Only in this last category did the  department chair who invited me also send me a "formal invitation" as a written letter on departmental letterhead stationery.  I have counted all of these as invited talks, even though only the last one had a formal written invitation, as in all cases, I was specifically asked and invited to give a presentation. "
A: One idea is to include expository talks to undergraduate and graduate students in the "Service" section of the CV. 
A: I think that the difference is between talks that you are asked to give (by whatever method) and things like "contributed paper sessions", where they solicit abstracts from people and everyone gives a talk.  Most AMS meetings have the latter.  Another example of a "non-invited talk" would be your PhD defense.
Certainly all the things you discuss count as invited talks for the purposes of a cv.
I personally just have a single "talks" section on my cv, but I'm a little selective about what goes in it (eg I don't include expository talks I sometimes give to grad students or talks I give in our local topology seminar).
