In Rome the two big sports are football (calcio) and basketball. For football you have a choice of two teams and they are Lazio and AS Roma. If you get the chance it can be worth going to see a game. Football is a true part of Italian culture just the same as cooking, wine and living with one's mama until in ones thirties is :) You can try http://www.ticketone.it/ for tickets to either of those two teams.
Basketball is a big passion also in Rome and across Italy and the Italian league has some good players and a good standard. You can also try and book via the Ticketone website for tickets and for Rome events accommodation, Holiday Velvet in Rome.