Sure they do.
Most people think hummingbirds make no noises at all. Untrue. Of course they all hum - you can hear them coming from several feet away. Their wings hum at 80 beats a second during regular flight, 200 beats/second during highspeed dives.
Most species of hummingbird (there are lots) have been observed to twitter and give static-like chase notes. Aside from this, though, there are some hummingbirds with actual songs, often very complex arrangements of notes, sort of like a high-pitched canary. To hear a recording, visit http://www.learner.org/jnorth/spring2001/species/humm/Update021501.html.
The mexican wedge-tailed sabrewing hummingbird engages in a lek courtship ritual. 15 or so males congregate in a bush and sing to attract the ladies. A hummingbird may sing for over a minute without pausing. Different songs are used to signify interest in a female and defiance towards another territory-invading male.
Their songs are a mixture of gurgles and squeaks, which sounded to one researcher like "a buzzing insect caught in a babbling brook." Steve Howell, in his Guide to the Birds of Mexico and Northern Central America, described it as "a loud, prolonged, gurgling warble interspersed with squeaky chipping, starting typically with hesitant, nasal, reedy, insect-like chippering which may go on for minutes before breaking into full song."
The only common American species known to sing is the Anna's. Most American hummingbirds do not sing but do have a series of specific squeaks. The ones without proper songs rely on their gorgets for courtship displays, and to threaten territory intruders.
There has not been a great deal of research on hummingbirds. They're small and quick and a bitch to catch, and the babies require feeding every ten minutes round the clock, due to their crazy metabolisms. Banding isn't a workable option, as their legs are too small to accommodate even the tiniest bands; plus, they are so lightweight, any band would upset their balance and interfere with flight.
So, it took quite a long time for hummingbirds to be investigated as thoroughly as other species. It wasn't until the early 90s that a hummingbird's brain was mapped. The coolest thing these scientists discovered was that hummingbirds' songs are learned.
This is not the case with most animals. Only humans, whales, dolphins, bats, and some birds are known to have the ability to learn vocalizations. If you take a kitten away from its mother, it's still going to say mew mew. Most animals can figure out what noises they're supposed to make without any parental help. Baby hummingbirds, taken away from their parents, would still know how to chirp, but they're also capable of learning a whole world of complicated combinations of sounds.
Vocal learning has been repeatedly demonstrated in two bird orders, Passeriformes (specifically, the oscine songbirds) and Psittaciformes (parrots), and, most recently, the Trochiliformes (hummingbirds). These three groups are widely separated from one another on the avian family tree, but their brains are quite similar. The same areas that control song learning and song production in songbirds and parrots are also present in the brains of hummingbirds. It was found that the songs of green hermit hummingbirds living in Costa Rica are different from those of the same species living in Trinidad. Weird.
http://www.wbu.com/edu/hummer.htm
http://www.mschloe.com/hummer/huminfo.htm
http://www.wvu.edu/~agexten/wildlife/hummer.PDF
http://web.missouri.edu/~multgord/wedge-tailed.shtml
http://www.amnh.org/naturalhistory/media/1000_media.html
http://www.amnh.org/naturalhistory/features/1000_feature.html
