I use the Canon EF 35-350mm 3.5-5.6L and have done for a few years now. Despite now being old and weighty it still serves me well, and I love it as a lens. That said, and I'm in agreement with MPowerM3 and Big Mike, it really isn't fast enough for sports photography. I have had some good results with it at sporting events, but these have been at outdoors on sunny days.
I totally agree with Big Mike's advice regarding choices of lens, especially if you want to do sports photography. If money is a factor, you're going to pay good money for an f2.8 L series lens, and you want a zoom with more than a maximum 200mm focal length, then the 35-350mm lens will do, but you're going to limit yourself at sporting events.
David