iOS/Android: Launching your camera app, switching to video mode, then pressing record often means the difference between catching a great moment and capturing the boring after-the-fact reactions. When you want to record a video on your phone, you want to record now. These two apps add an instant-record button to your Android or iPhone home screen.
The first, for iOS, is called Capture. It's $1.19 in the app store, and after installing it, you tap the Capture app and it instantly starts recording.
The second, for Android, is called QikCam. It's free in the Android Market, and it provides you with home screen widgets that, once set up, go straight from launch to record.
Capture seems to work quite well. I've got some complaints with QikCam (recording quality is low compared to my Android phone's default camera app), but it's the only app of its kind I was able to find on the Market. (If you find a better one, let's hear it in the comments.) Both will hopefully keep you from missing the best moments when you need to start recording 10 seconds ago.
QikCam [Android Market]