I noticed yesterday that one of my rear door seals was hanging off the body. Is there a certain adhesive I should use to put it back up or can I use general silicone sealant? I was told to get it replaced, but there's nothing wrong with it (besides it coming off the car).

 

well, sometimes these Rubber Shrinks over time. It gets shorter and pops off.
Your best bet is to remove it completely, and reinstall it with Weather Strip Adhesive they sell in part store.

No, you do NOT need to replace it.