Do: Boneless meat, pitless fruit, bits of food you scraped off dishes before/while washing
Don't: Noodles, rice, banana skins, potato skins, avocado skins, fruit pits, bones
There seems to be some controversy over whether or not eggshells can be put in the disposal, some people say you can, others say you can't. I think it's an "at your own risk" thing, because I do it and haven't had a problem, but I don't do it on a regular basis. I wouldn't want it to malfunction and wind up footing the bill for a busted disposal. since people have their own opions, fyi, eggs shells do sharpen the blades of the disposal.
That's from Answers.com... basically, anything fibrous like asparagus, celery, banana skins that can wrap around the blades is a no-no. All bones are a no-no, as well. Obviously anything that's hard (pits)... but if in doubt, ask your plumber!
PS I'm not sure why potato skins can't go in there and if you chop stuff up, it's better for your disposal.
Edit: I always put my coffee grinds down the sink.