Plenty of parents say yes, and there are now DVDs and children's classes being offered for children as early as 18 months.
Experts say there are some benefits: sports teach coordination, structure and sportsmanship.
However there are more downsides to early sports competition, according to most officials.
They say toddlers are at a unique risk for physical injury because their joints are not flexible yet. Their heads are large for their bodies, making them unstable, and they don't have protective reflexes developed.
Emotionally, they're not ready for competitive play either. Young children have short attention spans, a limited tolerance for conflict in winning or losing, and they lack disciplined for repetition.
It's also the age of creativity and curiosity, so experts fear forcing a sport on them can stifle their imaginations.
So instead of enrolling your tiny tot in soccer class, gymnastics, tee-ball or ice skating between ages 2-5, consider having them take classes where it's an activity, not a game with winners and losers.
Have your child do running, kicking, climbing and tumbling in a NON competitive environment, one that encourages their effort or where everybody gets a certificate or trophy.
Experts also suggest limited parental involvement at very young ages since parents often get too aggressive.
Check the American Academy of Pediatrics for more ideas on when and how to start your young child in sports.