Never fear, ye downtrodden masses, perfect pitch is acquirable!

I decided a year or two ago that I'd try to train myself into getting perfect pitch. Though I'm not close to the level a natural is at, I'm much better at telling pitches (without relative notes to help) than I used to be. The most helpful advice to me came from someone with perfect pitch. She said that to her, notes had a "color," and discerning pitch was the same process to her as discerning color. I don't know why, but after hearing that, I started being able to tell the pitch of single notes with much greater accuracy. I still can't listen to a piece and catch the pitch of every note, but I'm fairly accurate with single-note, slow melodies.
Some physical thing to try is to close your eyes and hit a random key on the piano. Try associating the pitch with a color, or flavor, or something else somewhat intangible. That will put your mind in the right direction, and after a while you'll probably just stumble into the correct way of thinking about pitch to identify notes correctly.
Now, it's probably near-impossible to get a studied perfect pitch to the same level as someone who naturally has it, but you can get reasonably close without a great deal of effort.
(And click Bernhard's link, it's very helpful)