The moon is so bright you can usually handhold the camera and still get really good shots, since the exposure is often 1/500 or faster, even with long lenses. I'm pretty sure
this and
this were both without a tripod (and both during the day, the second was just fast enough that the blue sky didn't expose at all). Also, fewer clouds will obviously give you sharper deatils and a better focus.
You still need a remote shutter though, just because they're so fun to play with. In trying to google the one I have, I couldn't find it, but it looks
exactly like
this except it says Opteron instead of Shoot on the top of it. So I don't know if thats a crappy knockoff, or they just changed brands. I think mine was a lot more expensive though. But it does all sorts of awesome timing things like time delays and interval shots so you can make cool time lapse videos and whatnot.