I've been going through the flooring/puzzle mat issue too. We just finished our basement, and I have berber over cement.
I recently bought [a href="http://www.amazon.com/Ironman-Deluxe-Flooring-System-2x2/dp/B000EJTEJ0/ref=sr_1_5?ie=UTF8&s=sporting-goods&qid=1211557013&sr=8-5"]Ironman[/a] puzzle mats. You put them together like a puzzle and can leave them out or put them away each time if you like. They're about an inch thick and very light.
They don't slide terribly, but they do travel a bit during a 60 minute step workout. Once I put my puzzle pieces together just the way I want them, I put heavy dumbbells on the corners. That helps a great deal.
Prior to using the mats, I had a lot of knee achiness from doing step on the berber alone. After purchasing the mats, the knee pain practically disappeared.
One thing about these that may or may not apply to other puzzle mats: I noticed my shoes were started to lose their grip on the Step. That was totally weird, and at first I couldn't figure out why (Though I could pivot like a madwoman!). The only new additions were the puzzle mats. I wiped them down, thinking there must be a coating on them that is getting on my shoes. Cleaned my Step and shoes too. That didn't help. BUT...covering my Step snugly with a beach towel took care of the problem. I now have great traction and can enjoy both the mats and the Step.
I figure whatever coating that is on the mats will eventually wear off. I noticed that after a weight day when I don't use the mats, my shoes go back to gripping the Step really well.