Generally speaking, I don't think it's a huge advantage in baseball because that's a slower game and the crowd just doesn't get loud for very long periods of time. In basketball and football, however, I think it's a bigger deal. And in college sports, I think it's huge. In college you have kids who get more amped up for games when they know they have their buddies and family members in the crowd, and they feed off the energy of the crowd in general. More adrenaline = a better effort. Also, in college you have motivating factors like knowing that you're playing your rival on national TV in "your house," and there's always the "we won't let them beat us in our house" mentality.
In the pros I think it's important, but not as important as college. In the pros there are some guys (not saying all, but some) who are just there for a paycheck, so I don't think you get the same effort from everyone in the pros like you do in college. It's still a big advantage though.
One only has to look at a team like the Seahawks -- they can, and have, beat some very good teams at home over the last few years, even though they are a bad team. Furthermore, they have one of the loudest stadiums and they usually lead the league in false starts by their opponents due to the crowd noise. But you take that same team on the road, and they are one of the worst road teams in the NFL. As an example, they beat SF 31-7 at home in week 1, yet they may very well lose by a similar score when they play them in SF.