I don't agree with Noam. I shouldn't have to struggle to figure out how the author went from point A to point B. I've spent far too many hours trying to understand the logical jump when the author says ``Clearly'' or ``Obviously''. On the other hand I don't want the authors to spell out every small algebraic manipulation either. And it's just completely infeasible to give a fully formal logical proof of even the simplest theorems.
So what level of proof should one give? As a general rule you should write for the reader. What would make it easier for him or her to understand your paper? When you leave out some details are you doing that because it would clutter your proof or because you are trying to save yourself some time. If it is the latter you do no one any favors.
Don't make assumptions of your readers. If you use a supposedly ``well-known'' technique, then either spell it out or make it clear what you are doing with a reference for those of us unfamilar with such techniques.
And how many times have you read ``the full details will appear in the final version'' where there are no later versions? Put those details in now. If you hit a proceedings page limit, have a full paper on the web with a footnote in the conference version pointing there.
If you do have a technically messy proof, the technicalities often overshadow the very pretty new ideas you needed for the proof. Be sure to also give a proof sketch that brings those ideas to light.
But mostly the Golden rule applies—Write your proofs as you would like others to write proofs for you.