This weekend I was at the International Students for Liberty conference where Peter Thiel gave the opening keynote. I asked him about PayPal's crypto-anarchist roots and the future of Bitcoin and currencies that might follow (in retrospect, I should have specified Bitcoin, because he was a bit vague with his response), and he seemed somewhat fond of the idea, hinted that some sort of cyber-currency future is inevitable, but said that Bitcoin isn't likely to have the network effects necessary to take off, and said that gold-backed currencies already have a great deal of support, and would serve as a better fit for a competing currency. He said that he would have more to say on the topic. Someone I talked to who attended a private social with Thiel mentioned there was an impression that Thiel hadn't done his homework when further questioned on the topic.

I don't have his exact response, but I know the event was taped, and suspect that videos will be uploaded by Students for Liberty after editing.

Edit1: CoinSpeculator shares details of a more in-depth discussion with Thiel
https://bitcointalk.org/index.php?topic=64610.msg760848#msg760848

Edit2: The official video of his response is up:
http://www.youtube.com/watch?v=5fsUMoHZ1cY#t=857s