Mosquitoes cannot lay eggs successfully in water that is constantly in motion. If your fountain has consistent water circulation, you may not need to add anything at all to your fountain. Reposition or remove any plants or decorative objects in or near your fountain that create still mini-pools of water for the mosquitoes. If you need to turn your fountain off for a period of time, such as during vacation, cover it or drain the water from it to prevent mosquitoes from using it as a breeding site in the interim.
If you have a large fountain that is at least 1 1/2 to 2 feet deep, mosquitofish (Gambusia affinis) are the best form of mosquito control. Mosquitofish look like female guppies, and just one fish can eat up to 100 mosquito larvae a day. You can usually obtain these fish from your local mosquito control office. You don't need very many -- about one fish per square foot of water surface. Goldfish, koi and minnows also provide some mosquito control but should not be placed in the same fountain as mosquitofish.
Completely changing the water in your fountain at least once a week eliminates any mosquito larvae or eggs growing in your fountain. If you don't want to waste water, use the old fountain water to irrigate your garden or water other plants. After you empty it, clean it with vinegar and a scrub brush before filling it with new water.
Mosquito dunks that contain Bacillus thuringiensis israelensis (Bti) are also effective. Bti is a soil bacterium that kills mosquito larvae when they eat it. It is nontoxic to people, mammals, birds and fish when used according to directions. You can find Bti in most home improvement and garden supply stores. Bti is different from Methoprene, another common mosquito larvicide. Methoprene is considered safe, but is not naturally occurring like Bti.