What would you want on a Lie theory cheat poster? For some long time now I've thought about making a poster-sized "cheat sheet" with all the data about Lie groups and their representations that I occasionally need to reference. It's a moving target, of course -- the more I learn, the more stuff I'd want to see on such a poster!
There are many obvious things I think everybody would agree should be there. The finite and affine Dynkin diagrams, with the Bourbaki numbering and also the coefficients of the simple roots in the highest root. The dimensions of the fundamental representations. Coordinate descriptions of each of the root systems, and of their Weyl groups. The exponents of each group, the Coxeter number, and the structure of the center. The exceptional isomorphisms of low-rank groups.
Only slightly less obvious: Satake diagrams. Dynkin's characterization of the nilpotents. Geometric descriptions of the partial flag manifolds $G/P$. The classification of real symmetric spaces.
One suggestion per answer, please, but otherwise, go wild! I'm not promising to actually make this thing in any timely manner, but would look to the votes on answers to prioritize what actually makes it onto the poster.
 A: Minuscule representations
A: Affine Dynkin diagrams (with the linear combination of simple roots that has norm 0)
A: Weyl Character formula and multiplicity formula for the weight spaces in a irreducible representation.  
A: Much of the rudimentary stuff requested above is accessible via an online sql database that I set up. It's at 
http://lie.math.okstate.edu/UMRK/UMRK.html
Don't be scared of the phrase "sql database". It is extremely easy to use for simple queries. For example, if you want to know how the Lie algebra E8 decomposes under its various maximal compact subalgebras you could get a table for that and more by simply filling out a form that passes the question to the database as an SQL query:
SELECT k , vogan_diagram , satake_diagram , k , krep_p , krep_k , rel_root_sys
FROM realform_data  
WHERE g='E8'
With just a smidgen of SQL experience it's equally easy to design correlative queries utilizing data from more than one table.
The UMRK database contains following tables:
g_data : data for simple complex Lie algebras (a la Bourbaki)
orbit_data : data for nilpotent orbits of simple complex Lie algebras
wrep_data : data for the irreducible representations of Weyl groups of simple complex Lie algebras
ss_data : data for the root subsystems of simple complex Lie algebras
levi_data :data for the Levi subsystems of simple complex Lie algebras
wcc_data : data for the conjugacy classes of Weyl groups of simple complex Lie algebras
realform_data : data for the real forms simple complex Lie algebras 
(BTW this thread was brought to my attention by Jeff Adams.) 
Birne Binegar
A: Description of the fibres of the Springer resolution. Classification of nilpotent orbits.
A: Probably you want the dual Coxeter number as well.
A: Moving quite a bit beyond the level of what is contained in Bourbaki's planches, one could ask for information about infinite-dimensional representations of Lie groups.
Ideally we would include a complete description of the unitary dual, but since this is still an open problem, how about an explicit as possible description of the tempered dual and the Plancherel formula.
A:  Edit: Per Noah's suggestion I have broken up my list into four separate posts, so this is the original post but with only one of the original list items.
For lack of a better term, "Quotient of Faithfulness" indicating for each fundamental representation what quotient of the simply-connected group the representation is a faithful representation of; this information is useful for questions of distinguishing between actions such as $Spin(k)$ vs. $SO(k)$ and determining whether a given reducible representation of $Spin(4n)$ is faithful (since it has no faithful irreducibles).
Awhile back I was also compiling some basics along the lines you are looking for. I also had a few other little facts that aren't widely known or used but that I was using in my research. My version was going to be in the form of a short pamphlet, but I think a nicely layed-out poster would definitely be very cool and useful.
A: Simple relationships between the fundamental representations (in terms of exterior powers of extremal fundamental representations based on a result of Adams)
A: Homology and homotopy groups
A: I know of a couple physicists with charts of 6j's hanging in their office. 
A: Adding to the listing of maximal subgroups, the decomposition of fundamental representations on restriction to a maximal subgroup
A: For each real form, the poset K_C\G/B, as calculable by the Atlas here.
A: Freudenthal's magic square of Lie algebras
and the corresponding square of projective planes:
ℝP2           
ℂP2          
ℍP2          
ↀP2
ℂP2      
(ℂ⊗ℂ)P2    
(ℂ⊗ℍ)P2    
(ℂ⊗ↀ)P2
ℍP2      
(ℍ⊗ℂ)P2   
(ℍ⊗ℍ)P2$   
(ℍ⊗ↀ)P2
ↀP2    
(ↀ⊗ℂ)P2   
(ↀ⊗ℍ)P2   
(ↀ⊗ↀ)P2
Also: have a look at John Baez's cheat sheet,
and at the subsections G2, F4, E6, E7, E8. 
A: Maximal compact subgroups
A: Real forms. And now I complain that Mathoverflow will not let me enter an answer with less than 15 characters.
A: For each Dynkin diagram, the involution taking a fundamental weight to its dual. (The main issue being that it's trivial for $D_{even}$, and nontrivial for $D_{odd}$. Mnemonic: what could happen with $D_4$?)
A: The Vogel plane.
.
Image stolen from Bruce Westbury
A: Finite subgroups
A: Maximal subgroups
A: Besides a magnifying glass and a very large empty wall for the poster, I'd like to have all relevant data (dimensions, Dynkin and Bala-Carter labels, ... ) for nilpotent orbits of the five exceptional Lie types including correct versions of the intricate closure ordering graphs worked out by Spaltenstein and others (reproduced in Carter's 1985 book with apparently some omitted edges for types $E_7, E_8$).  And of course designation of the *special" nilpotent orbits, Richardson orbits, etc.    
Actually, a reliable online database for all items mentioned in the answers here would be even better than a poster.
A: Types of the fundamental representations (real, complex, or quaternionic)
A: Handy identities for rings associated to Lie groups and algebraic groups, such as the enveloping algebra, hyperalgebra, or quantum groups of various kinds. For example, I often find myself needing to look up commutation relations between generators for these rings as in Lusztig's papers.
A: Combinatorial presentations of the cohomology rings of $G/P$'s. (And equivariant cohomology, and $K$-theory, and quantum cohomology ... Maybe this should be a second poster?) 
A: I am surprised nobody so far has mentioned Hecke algebras. I don't know what exactly to write about them -- defnition? finite, affine and double Hecke algebras?, Kazhdan-Lusztig basis (in some form)? geometric realization (say via the Steinberg variety)?
A: Their Stiefel manifold torsors.
