The classic
You are standing in front of two doors, with a guard in front of each. One door leads to safety and one to certain death - one guard always tells the truth, and one guard always lies. You do not know which guard is which. You can ask one question. What do you ask in order to work out which door is safe to go through, regardless of which guard you ask?

(I'm sure some smartarse will put the answer in the replies soon enough)
( Hdjejjwsjdjjf LOOK, Fri 14 Oct 2011, 1:01, 10 replies)

The real question is
which episode of Doctor Who did this question appear in?
( argyleblanket The man on the roof works for me, Fri 14 Oct 2011, 1:17, closed)

Pyramids of mars, episode 4, www.youtube.com/watch?v=FUNYn0jJPvg at the 10.00 minutes point. Didn't you watch any classic TV in 1975? Or more to the point were you even alive, oh dear!
(Benzyl, Tue 18 Oct 2011, 2:03, closed)

You ask a guard which door the other one would say was the door to certain death.
You go through that door.

This is assuming you want to live.
( 4Q just lurking, Fri 14 Oct 2011, 1:36, closed)

Wrong way round!
(Zachariah Pardon, pardon. J'AI UNE POUSSETTE, Wed 19 Oct 2011, 13:26, closed)

The Goblin King knows

(CactusZack Shaved his coin purse on, Fri 14 Oct 2011, 4:25, closed)

"Could you please both open your doors for me? I'd like to have a look through."
Failing that, "have you ever seen Labyrinth?"
( monster munch person, man, woman... camera... TV?, Fri 14 Oct 2011, 9:04, closed)

what's 1+1
(feedingtimeatthezoo day 1 of his bikini diet started, Fri 14 Oct 2011, 13:11, closed)

but
that doesn't help you find out which door is which, and you're not allowed to ask another question
(SarcasticBarSteward wants to be good at Photoshop when he grows up, Fri 14 Oct 2011, 18:20, closed)

I like the Terry Pratchett version of this one.
The answer is something like : Walk up to one guard, brandish a large axe under his nose and say unto him "Which is the safe door? And don't try getting clever because you're going through it first."
(Big D, Sat 15 Oct 2011, 0:12, closed)

The solution
tvtropes.org/pmwiki/pmwiki.php/Main/KnightsAndKnaves
Its all there I can't be bothered to cut and paste/pretend I'm that clever.
(KETCHUP, Sat 15 Oct 2011, 15:55, closed)