Rampant Games - What is a Roguelike?

Jay Barnson asks an interesting question - what is a roguelike?  I suspect this is a bit like defining the term "RPG" - it sounds easy at first but tends to slip of your grasp easily:

What is a "roguelike?" And where can the roguelike genre be taken from here?

I'm not talking about the Wikipedia definition, though it's a good start. I've got a fairly broad definition, myself - a roguelike is an RPG (see my scientifically and syntactically and legally robust definition of an RPG here) with randomly generated geography and other content. But even that definition is awfully squishy.