Window Air Conditioners
If your basement has windows, a window unit is a quick solution to get your basement cool and comfortable. Most window air conditioners are made to accommodate existing electrical outlets and circuitry, which is another plus. You'll also avoid installation costs because most models are easy enough to install yourself. The key consideration is that there is enough clearance between the bottom of the unit and the ground outside so that moisture from the unit can drain properly.
A wall unit is a good choice for just about any size basement. If your basement is large this might be a better choice, as wall units have even more cooling capacity than window units. You will need a professional assess your basement, walls and exterior to make sure your home can accommodate a wall unit. The walls must be able to support the weight of the unit, and like window units there must be sufficient clearance between the unit and the ground.
Portable Air Conditioners
With a portable air conditioner you don't have to worry about where it will go. You can also wheel them from one room to the next. You can be chilling out in your basement one minute, and then move the portable air conditioner to stay cool while working on a project in your garage.
Heat pumps pull the warm air out of the basement, convert it into hot water and send cool air into the room. In mild climates such as Texas and Georgia, where the temperatures more frequently stay above 40 degrees Fahrenheit, you can use a heat pump system to provide both cooling and heating. In addition to an air conditioner, you get a free hot water heater and room heater.