Latex foam mattresses have been around a long time. They are now very popular in Europe and becoming more popular in the United States. Positive: Long lasting (20-40+ years), offers support similar to memory foam, hypoallergenic, made with natural materials (usually), does not outgass; does not transmit movement to partners, insulative (warm), naturally resists dust and dust mites. Minuses: Can mildew or mold if not properly ventilated, sensitive to spills, heavy to move, fairly expensive, does not "bounce".
Latex foam is a product made from the sap of rubber trees ("100% natural") or can be synthetically created from petroleum, or be made as a combination of natural and synthetic materials. There are two techniques for creating foam for mattresses, the dunlop and talalay methods. Although talalay latex is more modern and costly to produce, the dunlop technique has been moderized as well. So they are both equally good.
Most mattresses sold are a combination of latex layers, e.g. "medium and firm" layers, though some are a single layer. The layers together usually add up to about 6" of latex, and sometimes up to 9" thick. To add thickness (often done aestetically) there are often added layers of polyurethane foam. Mattresses are encased in cotton, wool, and sometimes are topped with memory foam. Cheaper ones are made using mostly low-density foam.
Denser foams are heavier and require more materials (expense) to make. About 3" of latex foam for a queen size bed is about 50 pounds. Thus a 9" thich queen bed would be around 150 pounds and very hard to move. Cheaper mattresses are made with less dense foams.
Observations when shopping: A lot of mattress companies selling latex encase the mattress in a "normal" looking case and add on pillow cushion tops etc. However, the inner latex will outlast the pillow cushion: Expect the polyester fill fibers to eventually break down before the latex does. Getting a "topper" or pillow cushion that can be washed (and eventually replaced) may be better. A topper is recommended to reduce sweating.
A 6" mattress online costs around $1000-$2000, depending on the materials and casing. Some sites (e.g. Foamorder.com) have "no brand" pricing and offer customization for layering, sizing (cut-to-order) or even having the right and left sides of a bed different desities. Mattresses can be ordered online and delivered via UPS or through other sites even "white glove" (into the house) delivery is available. Which might be advisable if you can't move 100 pounds yourself.