You can use Cycorder without having the iPhone screen ON. You simply start recording, then press the lockscreen button on top of the phone and the screen shuts off but the camera still records video. Unfortunately Cycorder does not work on the 3gs.
On the native 3gs video recorder, the camera stops recording video as soon as you press the lockscreen button and the screen turns off. Not a huge problem but the light from the iPhone screen can be distracting in some settings (plus you to worry about accidentially pressing the STOP button on the screen) so it was nice to have to option of turning the screen off while recording.