"You need cover or concealment in order to attempt a Hide check. Total cover or total concealment usually (but not always; see Special, below) obviates the need for a Hide check, since nothing can see you anyway."
Cover is easy, it's just an adjudication on the environment between the Hider and the Spotter. And once in cover, it would be fair to say that a Hider no longer needs to make Hide checks as long as he stays in cover relative to the Spotter (Move Silently and Listen are different things altogether of course).
Concealment is tougher. Obvious effects like fog, heavy rain, smoke etc., as well as more dramatic effects like invisibility can provide anything from partial to total concealment, but the quality of the light is also a significant factor. Light quality ranges from Bright (no concealment) through Shadowy (partial concealment, or just 'concealment') to Darkness (total concealment). In either of the latter two cases a character can make a Hide check.
Suddenly, the adjudication of light sources in a dungeon can become extremely important, although the SRD has a table making things relatively easy for the DM. (And how wonderful would it be for the maps in software like Fantasy Grounds to show degrees of illumination around torches and other light sources?).
Edit: As one of my players has been quick to point out, the rules also state that:
"If people are observing you, even casually, you can’t hide. You can run around a corner or behind cover so that you’re out of sight and then hide, but the others then know at least where you went."
I have problems with this ruling because both 'observed' and 'casually' are ill-defined. I don't see any particular reason, for example, why a Rogue can't slip into the shadows of a darkened room even if he's being watched... however, that's probably what a distraction is for:
"You can use Bluff to help you hide. A successful Bluff check can give you the momentary diversion you need to attempt a Hide check while people are aware of you."
Again, adjudicating a distraction is difficult with such a wide-open canvas, but let's put the pressure back on the player a little. If she wants to distract someone - or more likely, multiple someone's - then let her make a suggestion on how she would do it. Ultimately, you may decide that there's no need for a Bluff check at all, if the circumstances are sufficiently diversionary, or you may decide that someone else in the party needs to make the check (for example the Bard may attempt to flatter a sentry into dropping his guard).
The only real conclusion to draw from this is that hiding is probably more difficult, and for certain much more situationally dependent, than we've been playing it up until now. Would strict adherence to these rules have had much of an impact on my campaign to this point? Probably not, but I can't help but feel that opportunities for cranking up the tension may have been missed.
More to come.