My girls LOVE dandelions from the yard....when they are "in season" (pesticide and bug free). They also like dried carrots. They weren't too thrilled with sweet potato or fresh carrots though. They go nuts for hay cubes (timothy alfalfa mix). They go through a lot of those. I also give them 1/2 tblspn of my chinchillas supplement once or twice a week too. It's got barley, oats, flax seed, crushed whole wheat (not a lot), oat groats, a little Animax and some other stuff in it. They love that.
I've given them sunflower seeds and peanuts, but due to the fat content I only give those on special occasions.
I don't really know of any things NOT to feed off the top of my head other than the obvious junk food that us humans like so much.