Originally Posted by TheOgre
The only advantage to attempting a field goal before 4th down is if there is a bad exchange. If the kicker never attempts the kick and the ball isn't turned over then the team can get another down to try a field goal. If the kicker actually attempts a kick though, you only get one try (barring a penalty).
I think there is also another exception. If the ball doesn't cross the line of scrimmage then it can be rekicked. That happened in a Pittsburgh game a couple years ago, but they may have changed the rule since then. I believe it was Reed who kicked the ball once only to have it blocked. It never passed the line of scrimmage and they got a chance to kick it again, and he made it.