In D&D 4e Eladrin get an ability called fey step which allows them to teleport 5 squares per encounter. Would an Eladrin be able to peek through a keyhole and bypass a door by teleporting?
Yes, if they can actually see through the keyhole.
From the RC, p214:
Line of Sight: The user of the teleportation power must have line of sight to the destination space.
No Line of Effect Required: Neither the user of the teleportation power nor the target needs line of effect to the destination space.
So as long as you can see the spot you're trying to teleport to, you can teleport there.
Whether you can actually see through the keyhole is a separate question. If you check the keyholes on most doors around you, I would bet that you can't use them to look into the area on the other side of the door. Generally the higher quality the lock, the less likely it is that you'll be able to see through it.