If you're looking for a sturdy, warm-season grass, you should consider buffalo grass. One drawback of this North American Plains native is that it's not the most aesthetically pleasing grass around, but that can be overlooked when taking into account the benefits of buffalo grass.
Similar to buffalo grass, carpet grass is also a good pick for problem lawns in warm-weather climates. Carpet grass tends to be used as filler since it grows in fast and dense, choking out weeds in the process. Other low-maintenance grasses for warmer climates are centipede grass and St. Augustine grass. The latter is best known for its ability to flourish and grow in shady spots, though it does require more care than other warm-weather grasses.
If you live down South, you've probably already seen what Bermuda grass look like. Although widely used in this region, Bermuda grass does send out runners all over the place. For cooler climates, the perennial rye grass is ideal if you plan on getting heavy use out of your lawn. If, however, you live in a cooler climate but want to invest time and care in a more luxurious grass, then the elegant bent grass is for you. Another cool season favorite is Kentucky bluegrass, which is distinguished by its fine blades and bright greenish-blue color. If you're in the market for a grass that will give your lawn that well-used look, even though you don't plan on using it all that often, the tall fescue grass is for you. Despite being a cool-weather grass, tall fescue is also used in more temperate climates. For a lawn that has the look of a lush carpet, fine fescue grass is the way to go. This cool-season grass is known for establishing itself quickly.