Yes they do but it's not their primary source of food. They eat mostly flies and butterflies, moths, wasps, bees, beatles and larve. Mosquitoes are like a snack for them.

Here's a list for insects and other animals.

Dragonflies and Damselflies
Both the larvae and adult stages of these insects prey on mosquito larvae and adults, respectively
Frogs and Tadpoles: Frogs and tadpoles consume mosquitoes as part of their diverse diet, which includes plant material, invertebrates, and other insect
Turtles: Aquatic and semiaquatic turtles eat all kinds of insects, including mosquitoes and their larvae, as part of their omnivorous diet
Purple Martins, Swallows and Nighthawks: These birds are known to consume large quantities of mosquitoes.
Other Birds: Many other bird species, including ducks, geese, and migratory songbirds, also eat mosquitoes
Lizards and Salamanders: Some lizards and salamanders also include mosquitoes in their diet.
Bats
Spiders
Fish

Feed meeeee, reeeee

Mosquitos save lives.

How many inner city youth decide to stay inside at night in the summer and not get into "trouble" because they don't wanna get bit up by mosquitoes