Sensitive plant aka Mimosa pudica is probably the one you are thinking of.* I saw this growing wild in the Amazon jungle.* It can become a weed in frost free areas if planted outside.
There is also the prayer plant aka Maranta leuconeura that folds its leaves up at night.* There is a very pretty red veined version and one that has blotches on it's leaves.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.