There are many properties that trigger after teleportation in 4e. Is it possible to activate a teleport power and choose the distance teleported to be 0 squares? (effectively teleporting in place?)
Though it is not explicitly called out, there is a preponderance of wording that suggests you must chose a destination space other than the current one.
... A teleportation power transports creatures or objects instantaneously from one location to another.
From one location to another. Strike 1 - Seems to exclude the same location - but depends on grammatical set theory. :-)
... Instantaneous: Teleportation takes no time. The target disappears and immediately appears in the destination that the teleporting creature chooses. The movement is unhindered by intervening creatures, objects, or terrain.
Blocking isn't a problem.
... Destination Space: The destination of the teleportation must be an unoccupied space that is at least the same size as the target.
Strike 2 - The destination space is occupied - by you.
... Immobilized or Restrained: Being immobilized or restrained doesn’t prevent a target from teleporting. If a target teleports away from a physical restraint, a monster’s grasp, or some other immobilizing effect that is located in a specific space, the target is no longer immobilized or restrained. Otherwise, the target teleports but is still immobilized or restrained when it reaches the destination space.
Teleport 0 is being used to escape restraint, this is Strike 3: You aren't teleporting away from restraint, so your are still restrained.
Despite all that, I imagine many DMs would house-rule otherwise, and I might be one of them.