For people interested in Antiquity, Trier has several ruins and two museums to offer. The ruins of the Imperial Baths and the Amphitheater are situated in the east, the Barbara Baths and the Roman bridge in the southwest, the Porta Nigra in the north and the reconstructed Basilica of Constantine in the east.
There's also the Rheinisches Landesmuseum, and finally, you should see Bischöfliches Dom- und Diözesanmuseum, close to the cathedral. This is the museum of the Archbishop of Trier. Its claim to fame is a splendid fresco (more), which is sufficient to pay a visit.
This museum was visited in a/o 2006, 2011.