Watch your background. Compose well in camera, but discuss with the primary shooter how tight she wants you to shoot for cropping into various size prints later. I habitually crop in camera very tightly, but I have to remind myself to be a tiny bit loose on weddings.
Try to be relaxed, but keep on your toes. Keep shooting. Don't let yourself get caught up trying to find the perfect shot to the point that you shoot too little. Keep shooting and have fun. Weddings are beautiful events and usually held in beautiful settings.
Try not to chimp (check your photos in camera) too much. It's good to confirm your exposure and such once in a while, but taking your eye out of the viewfinder means missed shots.
Don't get stuck on a single shot of some detail or artsy shot if it means you will miss the money shots you have to have. Again, keep cool and keep moving and shooting.
Don't be afraid to go where you need to to get the shot, within reason. Discuss this with the primary shooter ahead of time. IMHO, it's fine to step out in front of guests to get a shot as long as you are quick and quiet. Just don't stand there all day long.
If you have extra gear, bring it. Even if it's a crappy kit lens, bring it because you never know when a primary lens or camera is going to break.
Be confident and professional. Outside of the actually ceremony, don't be afraid to direct people a little to get the shots you need when appropriate.
Keep your head turning and keep shooting. Don't limit yourself to preplanned shots. Try to document every part of the pre-wedding, wedding and reception that you can.
Hey, sorry for such a rambling post. I'm pretty tired right now. Good luck and have fun.