I've tried to make felt balls before but I really didn't like the process - gather felt, roll into ball, dip into hot and sudsy water *over and over* until the shape holds and is hard - which for me, at a little over 10 minutes/ball, wasn't really fun. Last week, I heard from a friend that there's a super-simple way to do them, it takes no time at all, and they come out needing only a tiny bit of neatening.
Wool for felting (sometimes called wool roving or wool tops)
Pair of pantyhose you don't mind giving up for this process
Felting needle, for the final neatening
Washing Machine, Dryer (dryer is optional)
There's also a nice tutorial from Martha Stewart Kids on how to make felt balls here.