Logic puzzles for you!

I wrote a puzzle today, and in correcting it, I discovered that it lends itself to a series of similar puzzles with intriguing variations. Have a crack at them yourself, and expect to see some spoilers if you view comments. I know that some of you won't be able to resist this.

Puzzle 1:

The sphinx crossed a secret chamber deep in the castle's basement, trying to keep a level head and ignore the sounds of battle coming from outside. Her friends would survive only if she could quickly find and disable their enemy's source of power. There was, she had been informed, only one path to that source. As she approached the three doors, each one in turn formed a mouth and spoke, then went silent and became again a plain, wooden door with a number on it.

The first door said, "Door two speaks truly and leads to doom."
The second door said, "Door three speaks truly and leads to power."
The third door said, "Door one lies and leads to power."

An inscription above them read, "At least one door speaks the truth."

( Puzzles two through four are behind the cut. )