Your weekly trash service will not take tires and most disposal facilities don't accept them. This makes them one of the hardest items to dispose of and why they are constantly littered along the road and found in vacant lots.
Scrap tires are a major health concern. Trapped water is a perfect breeding ground for mosquitoes and can increase their reproduction rate up to 100%! Decomposing or burning tires also release hazardous chemicals and gases.
Although they seem difficult to dispose of, they are not. Most stores (Walmart, Firestone, etc.) that install tires will accept used tires for a fee, but be aware there may be a limit. Some transfer stations or landfills might accept them, but they cannot place them in the ground.
Recycled tire are used for many different things: mulch, playground bedding, roads, roofing, fuel, artificial reefs, clothing, etc.
Another option is to repurpose the tires. Simply Google "used tire uses" or "used tire projects" and you can stay busy all day!