A few credit card companies offered this in the mid-2000s (Providian and Citi, possibly more), but it seems to have fallen out of favor in the intervening time. I liked to have it as an option, so I'm glad it's making a comeback.

Since no one has mentioned it, American Express had Private Payments from 2000-2004, which generated one-time credit card numbers that the merchant could charge for up to a month.

Discover had "online card numbers" like this back in 2010. I'm not sure when they were originally introduced, though.

Citi offers this, and I believe bank of America as well.

Blur from Abine.com has an almost identical system to the one described here.