No, I didn't actually ditch my bed. I have a mattress and boxspring.
What I do not have (and haven't had for about 3 years) is a bed frame. I hate having to clean under the bed. My cats thought that black lining on the underside of the boxspring was made for ripping holes in and sleeping in like a hammock.
So, after removing that annoying fabric, I put both mattress and boxspring on the floor and sold the bed frame. At the time, I'd intended on replacing it with something I liked better, but then I realized: I like having my mattress on the floor. It makes getting out of bed easy, my cats don't get underneath it, my nightstand/two-shelf bookshelf is the perfect height, my bedroom seems bigger and airier, and making the bed look neat on the quick is so easy.
Maybe it's normal for most people to have a bed frame. I don't know. But I know what I like, and I hope I can always have a mattress on the floor! :)
P.S. Ideally, I'd like to try a futon and sleep on the floor, but I know that I really love a soft sleeping surface, and futons are meant for people who like a firm mattress.
