Richard Garriott, the designer of the Ultima computer games and Tabula Rasa, once said that his job as a game designer was to make sure that at least one solution to a problem was possible without preventing the player from finding other solutions on their own. For example, if you find a locked door in an Ultima game then there will be a key for that door somewhere. But you could also hack your way through it; or pick the lock; or pull a cannon up to it and blow it away.
Warren Spector, who started working with Garriott on Ultima VI, would later go on to design Deus Ex. He follows the same design philosophy and speaks glowingly of the thrill he would get watching someone play his game and thinking, "Wait... is that going to work?"
When designing an adventure, I actually try to take this design philosophy one step further: For any given problem, I make sure there's at least one solution and remain completely open to any solutions the players might come up with on their own.
Sounds like excellent advice to me. And there's a lot more where that came from, so be sure to read the whole thing.
(Promised herring later tonight or tomorrow, depending on how late birthday festivities go. ;) )