Options are many.
First, you might consider a japanese-style futon, which is usually used on the floor. But, you need to beat it and air it out regularly (that's how it's supposed to be kept). Usually, this is part of the process of putting the beds away for the day in the traditional way that japanese people used to live.
Second, you might consider getting an organic mattress. I had one from the Organic Mattress Store in Hellertown, PA. Great beds, lots of options.
For this sort of bed, it needs to have air flow around it (it's too heavy to beat out like a japanese futon). Thus, you want to create some kind of platform for it. The most simple is to take 2x4s the width of your bed, and get a number of them to run the length. You'll want to sand them down so that they won't snag your mattress. In my case, I opted to "gift wrap" each one in muslin fabric and with good adhesive. It actually worked really well and looked pretty nice, too.
Ikea also has sustainable/organic mattresses that are less expensive, so those are worth a look as well. They also sell a lot of differnet kinds of slat bed frames that are great for these kinds of mattresses.
We have a Design Mobel/Okooko organic mattress with a sustainably harvested bed frame (and headboard). I love this bed. It's my second organic mattress (went ahead and left the other one in the US), and I highly recommend them.
And, they are expensive. So, be prepared for sticker shock.