Personal favorites: Photoshop and XSI (now Softimage)
I've used those two professionally for both 2D and 3D, but they're both pretty expensive. Also use Maya, which isn't bad, and trueSpace, which is now free. I don't know how it fares now, but when I used it back in 2000 for work, it was terrible for animation.
There are some softwares specifically made for palettized pixel art, but I can't for the life of me remember what they were. If I remember, I'll come back to mention them.
Flash isn't bad for animation, either. If a game can utilize PNG files, Flash can output nice quality PNGs from your vector art. Personally, I find Flash to be a bitch to work in, tho, and it's not great to do pencil tests in for traditionally animated frames.
For such cases I've used a program called Comicart CG Animater, which is Japanese software. It's a rebranded version of animation software originally made by portalgraphics, makers of openCanvas. It's not the best, but for pencil tests I haven't found a piece of software that I've found more comfortable to use.