Pretty simple. Achievements that aren't revealed until you get them.
Here's a little mockup of what it would look like.
When you mouse over them it would simply display the name of the achievement and hidden as the requirement. There would be no prerequisites for these types of achievements. When you get the achievement it would light up and show the picture like any other achievement, and show what you did to earn it.
An example of what one of those achievements would be 'Give a Hug' - be blown up by a creeper. Probably unpleasant the first time, but hey, you got rewarded with an achievement! - plus that means that (usually) you won't go out of your way to do so, but it's likely to happen eventually.
Feel free to post any ideas or what you think would be appropriate achievements to be hidden.
Thanks for the support!
I also thought of another way to implement hidden achievements. Sort of how feats of strength work in WoW/SC2. These achievements wouldn't even show a spot on the interface until it's achieved. The only achievements that would show up like this would be things like being flagged for alpha/beta accounts. At least that's my preference for that - personally I would prefer the system I first suggested in this thread for the most part.