Since this is your first dSLR, I would skip the higher end cameras that EcoSee is recommending. Get a Nikon D40, D40x, or D60, with the kit lens. The 18-55 mm kit lens that comes with the D40 and D40x is an excellent piece of glass. I use this kit for all of my grab shots and as a backup to my main camera. The lens that comes with the D60 is essentially the same, with Vibration Reduction (Image Stabilization in Canon parlance).
The D40 doesn't have all of the bells and whistles that the more expensive camera have, but if you're just starting out in the the dSLR world, then that can be an advantage. You still have control of the most important aspects of the image, without a lot of extra options that might confuse you.
As far as Canons go, you could either get the XTi or the newly released XSi.
I just checked Wolf Camera
for pricing, and they have several of the cameras mentioned in this thread for under $1000. If I were making your decision today, I would go with either the Canon XTi or the Nikon D40x and use the extra money from your budget to either get another lens, a tripod, or stick it in savings for when you decide to upgrade.