Hi Susan,
I believe some people use just the foam in their basement. I personally have a two layer system in mine. I have 3/4" thick rubber "Cow Mats" or "Horse Stall Mats" that I got at Farm & Fleet. These are 4'X 8' each and weigh about 100 pounds. These mats are very hard and have a very fast response to impact. (i.e. if I drop a dumbell on it the dumbell bounces really high as opposed to if I drop it on the concrete). I then put the foam mats that everyone here is talking about over the rubber mats. The foam mats make the floor cushiony and comfortable.
The 3/4" mats are probably a bit over kill seeing as I have the foam mats over them, but I was concerned the foam mats wouldn't be supportive enough. They do make thinner rubber mats that would probably do the trick under the foam mats and would be a bit lighter and easier to get into the basement. I know the rubber mats will last 10 of my lifetimes. I have a feeling the foam mats will eventually need replacing, but if you get them at Sam's club or Costco they are reasonably enough priced that it's no big deal to have to replace them.
I hope this helps.
Dawn