Gas heaters (Natural gas and propane) These are the most powerful heaters. They will heat the pool fast and to high temperatures. If you want to heat a pool during cold weather or be able to heat a pool on short notice this is the heater to have. They are, though, the most expensive heaters to run and, if used irresponsibly, they can be very expensive to run. Bad water chemistry can destroy a heat exchanger quickly, (something not covered under warranties), so keeping your chemistry right is very important.
Heat pumps These heaters require more of an initial investment than gas heaters but they are more economical to run. In most cases, the difference in price can be recouped within a couple of years. On the downside, they are not as fast as gas heaters and will not work when temperatures dip to 41°F or below. These heaters are great if you are interested in maintaining your pool water at a reasonable, constant temperature. It is a lot more resistant to high alkalinity than regular heaters.
Solar heat Expensive up front but runs virtually free. Limited on heating a pool especially if there is not enough sunshine. Installs on the roof and must face southward. Great if you are interested in maintaining your pool a little warmer than normal. Great in cases where the pool itself is not in the sun long enough to get warm. They will also cool the water if ran at night.
Solar covers These are bubble rap type covers that float on the pool and prevent heat from escaping from the surface of the water. They will also increase pool water temperature somewhat if left on the pool long enough (days) Inexpensive and good to have especially in conjunction with a heater but very troublesome to handle and store.