I'm looking at getting a free video player from the Market but not sure which one is the best. It needs to be able to play .mov files.

Any advice?

I would say VitalPlayer if you must use free. otherwise I personally prefer vPlayer.

Mobo Player or Arc Media for me.

Arc Media especially if you are watching longer video files (say 45 minute US TV show) as its the only one I've found which stops the lip sync going way out.

I find it is best just to try them all as they all behave differently.

qqplayer is quite good.

http://qqplayer.software.informer.com/

I'll 2nd QQPlayer.

I was far more efficient at its job that any others I tried.