I just want to say that I'm very glad for the views and opinions expressed all around. I've gotten many great points and much to consider. I totally get the idea of a child wanting their personal space.
I think that my current views lie close to Zoebird's, although I don't know how much implementation I can accomplish. I would not force the children to any one way of living/sleeping arrangement, especially one that haven't grown up with.
As I mentioned, up until now, my 2 daughters (13 and 8) have had to share a twin bed, at least officially, and all three children have always shared one room. In the course of the years, we've ended up with all three on the floor, 1 or more of them in the living, on the sofa or floor, on our bed, on the floor in our room, etc. When my ankle was fractured a couple months ago, I spent a few weeks on the sofa so I could elevate my leg. And DH and all the kids decided to sleep together on the living room floor. So, they really haven't had their own personal space up until now and if we went to no-beds, it wouldn't be a huge change for them. It would be more so for me because of my concept that everyone should have a traditional bedroom.
In talking with the kids, my younger two have expressed that they think it would be great to have some kind of bed on the floor. In their view, they could just fold it up in the morning and have all that floor space to play. My oldest daughter says that she would like either a futon or a loft bed. So, that may be where we end up. I haven't found anything on Craig's list yet, so who knows when we'll make a change.
Please feel free to offer more ideas and opinions. They are helping me tremendously and I'm sure are of great help to anyone in a similar situation following this thread.