Ladybugs, parasitic wasps, bigeyed bugs, damsel bugs, minute pirate bugs, and syrphid flies eat aphids.
More Info: Aphids have a variety of natural enemies that enjoy them as a food source including two species of ladybeetles, the convergent and seven spotted ladybeetle. The parasitic wasp, often called the aphid parasite, is one of the more tenacious enemies, laying its eggs inside of the aphid body to hatch into larvae and eat their way out of the aphid.
Another natural enemy of the aphid are fungal diseases such as the Entomopthora fungi that after ingested infects the aphids turning them to change colors and then shrivel up and die. 
How Do Parasitic Wasps Kill Aphids?
Adult female parasitic wasps kill aphids by injecting an egg into the abdomen of the aphid. Within two days, the aphid dies as the larva grows larger inside the abdomen. The larva eats the aphid from the inside out, taking all necessary sustenance for growth. On average, parasitic wasps can inject eggs into up to 15 aphids per day, each day of their eight-day life cycle. The injected aphid’s body will be swollen and produce a color change. After 8 to 10 days, the pupa becomes an adult and eats a hole in the aphid’s abdomen to escape.
Do Ants Eat Aphids?
Ants do not eat aphids; actually, they protect them from predators. Ants eat the sticky, sweet excretions of the aphids, called honeydew. Some ants will herd aphids and will transport the aphids to a new food source if the one that they are feeding on is not sufficient enough in nutrients. Ants will also transport and store aphid eggs in their nests for the winter and then will carry the newborn aphids back to plants for feeding in the spring. Ants have even been known to kill the larvae of aphid predators while in their protective role.
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“Parasitic wasp.” Entomology at Texas A&M University – Home. N.p., n.d. Web. 29 June 2011. <http://insects.tamu.edu/fieldguide/cimg329.html>.
“University of Kentucky Department of Entomology — Mystery Bug Answers.” University of Kentucky – Welcome to the University of Kentucky. N.p., n.d. Web. 29 June 2011. <http://www.uky.edu/Ag/Entomology/ythfacts/mystery/mystry43.htm>.