The guys at WoW have done market research on this, and reckoned that a success rate of about 70% was optimal. That seems about right to me.
However, I would think that that's success rate for the adventure, which probably correlates to the 'tough' fights - against the BBEG and/or his most powerful allies. Since these represent the minority of encounters, the success rate for the 'typical' encounter should actually be higher - close to 100% for a rested party who don't do something stupid.
(Ideally, against the BBEG, they should have a 70% chance of success if they're either lucky or skilled. If both, it should shift to close to 100%. If they're neither lucky nor skilled, then the rate should drop to no higher than 50%, while if they're actively bad then the rate should be close to 0%.)
Of course, all of this discussion is strictly "behind the scenes" stuff. One thing I absolutely don't want is for these probabilities becoming visible to me as a player, and while the DM can and should be giving some thought to this, he should probably never mention it to the players.