I had a mattress that I had directly on a cement floor in a basement. That was an expensive mistake. The mattress retained moisture because it couldn't breath, contributing to it collapsing. A basic bed frame is cheap, makes the room look nicer, and provides extra storage space underneath.
I've been having some fun with my current setup. I have a bed, nightstand, desk, dresser, and closet in one room. It's maybe a little cozy, but functional as long as I put some thought into it. I even have a nice space in the middle that I can pretend I use to work out in.