Modern Jordan is an interesting country but the major attractions come from the historic Jordan:
Petra: It's without any doubt the most famous and even the most beautiful place in Jordan to visit. It is not only the fantastic job of the Nabathean architects but even the fascination of the colourfull sandstone itself that makes it so unique.
Petra is an old greek name and means "rock".
Quseir 'Amra: not very much known Quseir 'Amra is as unique as Petra but of different kind. It is the name of an Omyyad castle located in the desert East of Amman. There are even others but none of them is like Quseir 'Amra. It is one of the most remarkable buildings of early muslim architecture. See the pictures and comments.
Wadi Rum: One of the most famous desert locations, not only in Jordan. Lot's of the desert szeneries of "Lawrence of Arabia" have been filmed here. It's desert at it's best.
The mosaiks from Mount Nebo: not only the famous map of ancient Palestine but even many other mosaiks found in the ruins of several churches in the Mt. Nebo region.