The first American space toilet was Alan Shepard's Space Suit. Because his flight was only supposed to last 15 minutes, there was no provision made for him to relieve himself in the capsule. However, because of numerous delays prior to takeoff, his flight was delayed for hours. The decision was made to Alan Shepard to relieve himself in his space suit, and continue with the mission as normal.
This problem prompted NASA to develop the first space toilet, a modified diaper. Diapers are still used by astronauts when they are outside the space shuttle, when they are wearing a spacesuit.

For more information about Alan Shepard, click here.