I have a Canon Rebel XSi and would like to know what settings take the best sports pictures. I am taking pictures of basketball.

Basketball is a very difficult sport to shoot, because it is indoors and that means low light, but fast moving subjects. Although your eye can adapt to the light and you think the court is "brightly lit" - there is very little light. No matter what settings you use, you may not be happy with the results. Pro photographers put strobes in the rafters over the arena, or use very high end cameras and lenses to shoot basketball.

That said, here's what you need to do:

1) Use the highest ISO setting.
2) Use AV mode and set your camera to the widest value (smallest f-stop number) your lens allows at the telephoto end. If you don't have a fast lens, you can greatly improve your photos by using a faster lens, i.e. 70-200mm f2.8 or 300 mm f2.8. This is why you see pro sports photographers shooting with those "white lenses" - those are the fast lenses that get the job done best.
3) Take a test shot before the game starts. Ideally your test shot is of a person on the court - an official, someone sweeping the court, etc.
4) Check the image on the review screen, and also look at the histogram. It may be underexposed due to the dark background.
5) Note the shutter speed.
6) Change to manual exposure mode. Make the settings the same as your test shot, then adjust the shutter speed if needed (if the test shot was underexposed, use a slower shutter speed setting in the manual mode shot.)
7) Take another test shot. Once you have dialed in your settings in manual mode, they should work for all photos on the court, as the lighting is usually very even all across the court. The settings will not be suitable for taking photos in different lighting such as the spectators.
8) Don't forget to change back to your regular settings when you are done!

#0 (before #1) - you should also shoot in RAW. If you have only been shooting in jpeg mode up to this point, you also need to make sure your workflow is setup to shoot in RAW. This is very, very important when shooting in extremely difficult lighting situations such as basketball. By doing your own raw conversion (instead of letting the camera do it for you in-camera) you can better control the conversion, the noise reduction settings, etc. You paid a lot of money for this camera and it's not wise to let the camera take the photo then throw out 90% of the data it just recorded and only save 10% in the jpeg file. For this reason, shooting in RAW should be part of your workflow for every shot, every shoot, not just for shooting basketball.