Willow loves Bonito flakes (basically pure dried fish) where as Odo likes junk food. Both of them like "We Pity the Kitty" treats which are basically freeze-dried chicken.
I think most of the greenies controversy comes from bad experiences with the dog variety--the dogs end up swallowing a piece that is too large, and it doesn't break down in the gut. It can cause a blockage. The cat treats seem to be completely different though.