I've run the gamut: thin folding foam mattress on the floor, cheap-ass Goodwill mattress on the floor, actual bed with frame, box springs, & mattress, cushy soft mattress, Tempur-pedic, firmer mattress, etc. When I was younger, I could tolerate sleeping on a mattress on the floor, but it was never comfortable, and getting up in the morning was a bitch. I sleep best on super-soft mattresses -- like floating in a cloud! -- but then I wake up with back pain. Sleeping on a thin foam mattress on the floor wreaked havoc on my joints, both during the night and the next day.
We actually just bought a new mattress, the firmest one I've ever voluntarily purchased. I sleep okay on it, and it doesn't mess up my back, but I can't say it's comfortable or that I sleep deeply on it. It's worth sacrificing quality of sleep for back maintenance. I just wish I didn't have to choose.
Even when I was a kid, though, I could not sleep on a bare floor, or even a carpeted one. That always hurt my joints and head too much.