Fascinating: It used to be thought that giraffes did not sleep at all, but this was shown to be incorrect in a 1956 study which demonstrated that adult giraffes slept recumbently on the ground for short periods (2.5-6 minutes), resting the head on the hindquarters or ground and holding the neck in an arced posture.
The sleep behavior of giraffes was also looked at in detail in a 1996 study which showed that giraffes slept both while standing and while recumbent for a total of 4.6 hours per 24 hours.
If you're interested in the sleeping behavior of other creatures, read "Sleep behaviour and sleep postures" at Tetrapod Zoology.