I've been using Flash CS4 to animate my characters and then export the individual frames. It's certainly a powerful tool but it's far from cheap (~$600 for retail though you can get it for less if you're a student). I've found CS4's bone/IK animation tool to be quite useful for quickly making good, fluid animations.
As for creating sprite sheets, I found this the other night after many hours of searching:
GlueIt.
It's a fairly simple tool that I've been using to stitch the frames Flash exports into sprite sheets. It does have some shortcomings and I'll probably just end up writing my own sprite sheet creation tool when I have some free time, but it gets the job done.