Well, it depends on how old it is, what materials it is made out of, and how it has been kept and used and maintained. When you look at the ones you come across, make sure you bring someone and have them help you check everywhere in that thing. Look for worn parts, rust, broken things- do a really good inspection. Check the electrics, all of the lights, the tires, the floor, the ceiling, etc. etc. etc. If you happen to know a person who is very knowledgeable about trailers, bring him or her, too!
Whenever you find a promising listing go and do research on that make and model, which might tell you what to look out for, as well as basic information that the seller might not have provided.
A good trailer that has been cared for properly will last for a very, very long time, so buying used is fine, just approach it like you would a used car. I would say the biggest things it to arm yourself with information and be thorough in your inspection. Good luck!