Originally posted by Whisker Barrel Cortex
Actually, both T1 and T2 are pretty much performed on every scan. I don't think I've seen one without the other. There are also many other techniques (proton density, FLAIR, STIR, FATSAT, etc) that are often used depending on the body part and clinical question at hand.
As for the advantages of one over the other, there are two many clinical uses and body parts to answer this broad question. In general, T1 is better for visualizing anatomy and T2 for pathology (this is VERY general).