I have a Canon T3i. I want to catch the kids while they play sports, so it needs to be good for distance, and of course, not super expensive!
Check Cannon website they have a lot of lens for sports shots. They are affordable compared to most.
You're probably looking for something like a 70-300mm zoom. It depends on the kind of sport as well. Is it indoor, outdoor, a slower sport, a fast moving sport? All of these factor in to the best choice for lens.
On the inexpensive side, you're probably good with this as a general zoom:
It's an f/4 so it's not going to be super great in dimly lit spaces. You'd want an f/2.x if you'll be shooting in a darker location. Also, the lower end the lens, the longer it's going to take to auto-focus.
This is a more expensive choice, but it's going to focus on a fast moving subject better.
Or you can go off-brand for less expensive options.
I also have a t3i and I use this lenses for all my sons soccer games.