Polyurethane foam is by far the most common material used in mattresses today. Accross the industry you will have trouble finding many beds without it. This is a petroleum based foam that is available in every durability, density and quality imaginable. It is a low cost material, and regardless of the price mattress you are looking at, is subject to some rules of durability. Newer to the market is Soy Foam, which is 5-15% soy oil, as opposed to 100% petroleum based; this is subject to the same levels of deterioration.
When shopping for a traditional coil innerspring mattress, or even an all foam mattress, here is what you should consider:
High quality polyfoam will break down 20% every five years on average (higher density lasts longer), and if the bed is a "no-flip" you will develop body impressions 20% the depth of the poly foam within only 5 years. If you can flip the mattress, you can keep the two sides mostly flat by rotating on a quarterly schedule.
You are forced to trust the salesperson representing the product with regards to the contruction of the mattress, and the depth of the foams within. You can verify, to some extent, the composition by looking the mattress tag for the construction materials )if it has no tag, it has no warranty, and you should probably not buy it). This can be frustrating however, because memory foam is also a polyurethane foam, and may be listed separately. They will also not have inches listed, but rather a percentage of the total mattress weight. If it is important to know the exact specification, ask to see a printout of them; if they will not provide them, they were probably misrepresenting the product initially (all retailers have access to these spec sheets).
Convoluted poly foam generally lasts longer. So will high density foam. These will be similarly inexpensive as a construction material.
Polyurethane foams can go by many names, including supersoft, quiltflex, soy foam, and many others. They are all going to have the same petroleum based composition, and will be sudject to the same body impressions.