Here in Costa Rica our home has 100's of geckos, and daily rain showers, making for an excellent experimental opportunity.  They can be as wet as you like and still stick to the ceiling quite well indeed. 

This capability is attributed to Van der Waals forces operating at molecular scale in the geckos' foot pads; see:

http://en.wikipedia.org/wiki/Van_der_Waals_force

My cat tried to duplicate this mechanism without success.

I have seen the creatures dash across a patio covered in a layer of rainwater and climb straight up a smooth wall. They do not have a problem at all.

As Jim and Stewart said, but remember that geckos have a need to deal with many kinds of surfaces, and cannot afford to fall every time they encounter something new. Not all of them use the same mechanism that Jim mentioned. Many use claws for example. Nor do the relevant parts of their feet easily get wet. So it is largely a question of what species of gecko you have in mind. There are hundreds.

As for geckos that use the delicate and elegant van der Waal's forces, you might find that they get frustrated by oily or dusty surfaces, but frankly I would be unwilling to try it myself and I hope that no one else will do so wantonly. I happen to be very fond of geckos.

Go well (up or down walls)

Jon