I agree with all the comments given--keep it simple, avoid tacky transitions/effects, shoot extra footage, etc.
Some other tips:
* Light is very important. Especially with consumer level camcorders. With still we have flash, with video we often do not have enough light. If you can, turn on lights and open blinds before you shoot.
* Get different angles, especially for kids. You don't want all the shots to be you standing, shooting down. Get at your daughter's level for some shots, show her prespective.
* Get stuff for cut-aways. After the action is over, shoot the toy she was playing with, her bike, books, crib/bed. For a sledding video get shots of just the sleds, their boots, etc. Just little clips that will give you a nice transisition from one scene to the next. Also get some establishing shots, the outside of the house, the entrance to the Zoo, etc.
* Mix in photos with music and ken burns. Breaks up video nicely.
* Make two versions of each movie - long and short. Think of it as your "director's cut". You and your wife will want all the memories you can get but your extended family and friends may get bored after 5 or so minutes. Make a short version that show just the highlites.
* Get a printer that can print directly on DVDs. Friends and family love this.
* Backup, backup, backup. If you are shooting to tape, you at least have that backup. If you are shooting to newer AVCHD cam, come up with a workflow that works for you. Backup your footage to DVD, external HD and maybe even online storage. These are family memories and you need to ensure you have them backed up.
* Have fun.