I love the events. I'm on the pit crew, so I spend a lot of time working with my own team on the robot (err...unfortunately) and such. But working in the pit is also fun in terms of working with other teams - you become pretty good neighbors with the teams next to you and you can see what everyone's working on.
Another fun part of the competitions is cheering. Hopefully your team likes to cheer and dance, because it's super fun if you get into it (and you can meet people from other teams
).
So it's really the social aspect that makes it such a great experience for me (at competitions, and also on Facebook and Twitter). Building robots is fun and educational and all, but it's even more fun with friends.