My husband takes a lot of macro pictures using his first gen Canon Digital Rebel EOS. It has served him well for many years now. He took an old lens and reversed it somehow, using an adapter. I'm sure that he could get into detail with you if you want to know how exactly he did it.
Here are some examples of his macros (they are mostly insects) on Flickr and the link to his photo stream:
Macro and DSLR have a lot more to do with the lenses than the camera, though a decent body doesn't hurt! What are you looking to use the camera for? If you just want good quality pictures, but not for professional use, a Canon rebel with a macro lens would suit your purpose well! I went with a Canon 50D as I wanted something that would would give me a little better quality in low light situations than the Rebels would.
As for lens suggestions, good macro lenses can be in the thousands, but you can buy a pretty decent one for $300 or $400. Your best bet would be to go to an actual camera store and ask to play around with different lenses. Also, do your research! There are a ton of good camera forums that have excellent reviews and samples of photos taken with the lenses.