Nichole,
You're having a hard time finding a sport for your 3 year old because that is too young for kids to play organized sports. Consider tumbling, movement or maybe gymnastics to get him physically (and mentally) mature enough for sports in a couple of years.

Most organized sports begin at the age of 5 yrs. old; although, if the kid is very active, and highly interested, some organizations allow kids to start at 4 yrs. old. It all depends on the kid and the rules of the organization you're attempting to place him. If you find an organization that will take him at 4, as a parent, you must evaluated and decide if your kid is physically and mentally ready to take on the tasks. Some kids do mature a lot faster than others.

Both comments above are right, most organized sports start at 5 yrs. old. However there is a soccer program in our area for tots, it's more like a play date, but it's organized by the local sports complex and I have to admit a riot to watch. Also even though it's not a organized sport, learn to swim programs are fun for kids and let's them learn with other tots their age under supervised insturction and kids love it. But best of all is just having play dates and let the kids go at it with wiffle balls, soccer balls in the back yard, that's how my kids got started in sports and it's a lot of fun for the kids and parents. Anyway just a interesting side note, Tiger Woods started golf at 3 and Mozart started playing piano at 3, both seem to have done pretty well in their choosen fields. Most important aspect to introducing a sport to a child, make it fun, fun, fun.

Ok these guys covered it pretty well so I'll just emphasize a few of their points. Organized teams at this age are few, but soccer seems to be a natural because it lets the kids do what they do naturally, run. Just make sure it's not a team that tries to be competitive, that will take the fun out of it for most kids this age, and fun is most important at this age. And most kids will love tumbling and swimming, and getting them those skills young can lead to lots of other sports interests later.