Alien Chao
Purchase a shiny green egg from the black market or trade with a friend to obtain one. Find a bunch of dragons and skeleton dogs (in case you don't get the right parts) and bring them into the garden the chao is at. Give your chao dragons until only the antennae are present, letting your chao have a skeleton dog every now and then to get rid of any uneccesary parts. If you teach the chao how to walk, it will look like an Alien! Whee! You can also make it metamorphosize for extra coolness, and give it any green animal parts (if you can tolerate and risk losting your antennae).
Hopping Bunny Chao
First, obtain a normal chao. Keep giving it rabbits and green drives until it has all parts of a bunny (ears, legs, paws, etc.). Raise it as a neutral chao, keep giving it bunnies after it metamorphosizes, and eventually it'll start hopping! Be sure to keep its levels even if you want to race it.
Total Tiger Chao
Obtain an Orange Chao and give it all Tiger Parts. Try to keep its run stats down so it'll continue to crawl. Another thing you can do is get a Black Chao from the market and give it all Tiger parts. It's not going to look as much like a Tiger as the latter chao did, but the Chao itself will match with the black Tiger stripes from the Tiger parts.