I don't know much about Trajan. Come to think of it, the only thing I do know is under his rule the Roman Empire was at its greatest extent (117 A.D.). Did he do anything really good? Was he just at the right place at the right time?

Trajan was a good military general, and IIRC a reliable historian (a good source of information of the Julio-Claudians and so forth Romans before him). But he did over-extend the empire, which is why the next emperor Hadrian had to give up some provinces, and greatly fortify others. He was also incredibly lucky to rule at a time when there were no great threats on the borders - the Germans were relatively settled, the Scythians / Sarmatians were friendly, Parthia was occupied on its other borders, and the Bedouins and Berbers were not highly interested in raiding the southern provinces. So in short, he did do a couple of things good, but a lot of that was due to being in the right place at the right time.