As has been mentioned, C and G are good keys for bass runs and capoing to the second fret gives you D and A which are handy for playing with fiddles or mandolins. Drop D tuning is great for the key of D and if you use a capo like a Shubb, you can capo the first five strings and leave the bottom string open for a drop E using D shapes. The nice thing about this is that you don't have to retune and you can use regular chord shapes above the capo.
Someone also mentioned that E and A are good for blues. G and D are pretty good too.
Swing tunes are usually played with closed chords that are altered and many substitutions are used.

I've heard C called the "people's key", G called the "key of astonishment" (Gee!) and A called the "Canadian key" (Eh?).