On my last visit to my parent's house, my mom bought a kumquat tree for her garden. As a result, I ended up going home with lots of beautiful kumquats! I've always enjoyed Kumquats, though I can only eat them in small quantities because of the tart flesh.
I'm not really sure why I enjoy them so much. I think it's because of how small and cute they look. Like baby oranges! Though they really don't taste anything like oranges. The outside skin is slightly sweet and the inside flesh is very, very sour. There are usually a few small seed inside. For anyone who has not eaten a kumquat raw, you simply pop the whole thing into your mouth: skin and all. Just spit out the seeds when you are done chewing.
I've seen kumquat recipes where people make them into candies, jams, etc to get rid of the tartness. I've had some candied preserved kumquats before, but I didn't really like it because I could no longer taste that it was a kumquat. So I still prefer them best in their simplest, natural raw form.
If you are looking for some interesting ways to eat kumquats though, I found a good site that provides a lot of recipes over at Kumquat Growers Inc.