I think the extra weight of a trailer is a handicap. That may vary though. If you choose heavy panniers and racks it can be just as bad. Some of the weight of a trailer is offset by a lighter bike if you use it with a road bike rather than a touring bike.
If you ride with others it is hard to draft behind a trailer.
It is a pain to fly with a bike and trailer. If you ship it instead it is another thing to ship.
I like the compartmentalization of multiple panniers.
Trailers are awkward to park in some places where space is limited.
I have heard of folks having problems with trailer handling on high speed descents (I have not seen this myself)
Trailers are easy to pack and carry a lot.
Trailers allow the use of a regular road bike (assuming low enough gearing).
Trailers seem to be preferred by many off road tourists.
Trailers can be quickly detatched to go ride unencumbered.