Advantages of a Trailer:
1)can carry more stuff
2)Reduces stress on wheels
3)Aerodynamic(I'd like to see more proof of this--noone's done a wind tunnel test)
4)Easier to disconnect load from bike.
5)Bike frame independent(for BOBs. Other trailers, not so much)
6)Great Off-Road Handling(single wheel trailers only)
Disadvantages of a Trailer:
1)Easy to carry too much stuff
2)heavier
3)extra rolling resistance
4)Poor low speed handling under heavy load
5)Instability at high speeds for light riders
6)travel issues(shipping trailer to start/endpoint of tour)