Any of the popular DSLR cameras would be good for portraits. Landscapes are usually easier with a wider view, so something will a 'full frame' sensor would be ideal...but way out of your price range. For sports, you will want fast shooting (high frames-per-second) and a big buffer.
Here is a side-by-side comparison of 4 cameras. From Canon, the Rebel XT and 30D....from Nikon, the D50 & D80.
One thing to note, is that the Canon 30D has the fasted frame rate, at 5.0 FPS. That would be good for sports.
The D80 is very new to the market, and looks to be a very good camera. Might be hard to find in stores though. I have a 20D (older model of the 30D) and I find it to be a great camera.
Of course, the right lens will also be a big help...so you might be better off getting a less expensive body and a better lens. The Rebel XT and D50 are both very good cameras as well.
A good thing to help your decision, would be to go into a store and hold the different cameras. The Rebel XT, for example is quite small. If that fits your hands, then that is a big plus. If it's too small, then look at a bigger camera (or consider a battery grip accessory).