Well, all of the stone (granite, marble, soapstone, travertine), concrete, recycled glass (IceStone, terrazzo, Vetrazzo), tile (ceramic, stone), engineered stone (Caesarstone, DuPont Zodiaq, Cambria Quartz), stainless steel, and solid surfacing (Corian, Avonite, Swanstone, Silestone, Livingstone) countertops have no or extremely low VOCs such that many are GreenGuard certified.
The durability of many of these materials is amazing, and many can be sanded or ground down if they are ever chipped or damaged in some way.
The real unknown with many of these countertops is not the counter itself, but the method used to attach it to the underlying substrate (usually epoxy or another adhesive), the makeup of the underlying substrate (often plywood containing urea-formaldehyde), and the sealer used to seal the top of the counter from common staining materials like wine, coffee, etc.
Some of the paper-based countertops are made with offgassing resins based on the chemical phenol and are much more easily damaged than the more durable materials listed above. Laminate countertops are much cheaper than all the other countertops mentioned here, but are not repairable if damaged, are made of plastics, and most often are attached to offgassing particleboard underlayments with VOC-laden adhesives.
As for the cost, none of these options except for the laminates are "cost efficient." Most will run you $6,000 to $10,000 -- or more -- for a typical-sized kitchen from a normal fabricator and installer. But you don't have to go with the typical installation, either.
On many of our projects, we go to the "bone yards" of local installers to look for remnants of granite slabs. Often the installers will heavily discount this material. You can have the fabricator cut, polish and install the materials. You also can do the work yourself by cutting and polishing the materials with simple tools you can buy at a stone fabricator store online for less than $200.
Another option is to visit a local building material salvage company. This option involves a lot of shopping around to find a remnant you like in a size that you can use, or you can just pick what is cheap and will work and go with it. Either way, you will save thousands of dollars off of buying it new.
You will also be supporting an industry that keeps hundreds of thousands of tons of construction and demolition debris out of our landfills and gives tens of thousands of Americans work. Sounds like a great way to save money and build a little bit of sweat equity in the process.
For more information:
You should read Lily Livingston's Q&A "I plan to replace my kitchen countertops and don't want to spend a lot of money. Any suggestions?"