Communication

Languages

"Anyone can speak Troll. All you have to do is point and grunt.."
    -- Fred Weasley

Judging by the fact that Barty Crouch Sr. speaks over 200 languages, both Muggle and Magical, it seems likely that there are magical ways for wizards to learn them.

Muggle Languages

English

Since Hogwarts is located in an English-speaking country, everyone there speaks that language. A number of dialects are evident, however, particularly from Hagrid. Seamus Finnigan speaks with an Irish brogue.

Bulgarian

The Bulgarian Minister of Magic, Mr. Oblansk, acted as though he couldn't speak English, only Bulgarian, letting Fudge stumble through the entire day of the Quidditch World Cup trying to make himself understood. After the match was over and Ireland won, Mr. Oblansk said, in perfectly good English, "Well, we fought bravely." Fudge was a little put out.

French

The students from Beauxbatons Academy spoke French. They managed English very well, however. One wonders how well students from Hogwarts would have fared had they been transported to Beauxbatons; there is no evidence of instruction in foreign languages at Hogwarts.

many other languages

Harry heard folks talking excitedly in other languages as they walked through the campground at the Quidditch World Cup (GF7)

Latin

the root language of many of the spell words

"I enjoy feeling that wizards would continue to use this dead language in their everyday life."
     -- J. K. Rowling (Sch2)

"It just amused me, the idea that wizards would still be using Latin as a living language, although it is, as scholars of Latin will know... I take great liberties with the language for spells. I see it as a kind of mutation that the wizards are using."
     -- J.K. Rowling (CBC)

Wizarding/Magical languages

Fairy

Fairies use what sounds like a form of buzzing to communicate among themselves (FB). Note that it is quite possible that fairies, like bats, have hearing that can pick up higher-pitched sounds than most humans can hear, so there may be more to fairy communication than the casual listener would notice.

Giant

The giants speak their own language; some do not speak English, and possibly do not speak any human language. However, enough surviving giants speak English that a translator can be found if the giants care to permit a visitor to communicate (OP20).

Gobbledegook

goblin language
"bladvak" means "axe" in Gobbledegook (GF24)

Mermish

Merfolk language used above water; Merfolk speak human languages underwater. It sounds like horrible screeching if heard in air.
Dumbledore can speak Mermish.

Parseltongue

Troll

The Trolls' crude form of language consists of grunts (from the viewpoint of a human listener, at any rate), although some can be trained to speak a few words of English (FB).