The Marauders: Moony, Wormtail, Padfoot, & Prongs

Group of students at Hogwarts 1971 - 1978.
House: Gryffindor (WBD).
Ringleaders: James Potter and Sirius Black.
also included: Remus Lupin and Peter Pettigrew.

The boys in this group were some of the most clever students attending Hogwarts at the time. They used their talents for, among other things, legendary feats of mischief. They created a map, called the Marauder's Map, which showed Hogwarts in every detail, including every passage and the location and movements of the denizens of the castle.

The nicknames for the four students came from their identities as Animagi. James transformed into a stag, hence the name Prongs. Sirius became a large dog (Padfoot) while Peter became a rat (Wormtail). Remus was not an Animagus; he was a werewolf; it was his monthly transformation into a wolf that earned him the nickname "Moony" and provided the impetus for the others to become Animagi.

Which House were they in?
Gryffindor. We know this from one of Jo's answers to a fan question in the World Book Day chat. However, the person who submitted the question listed Lupin's name twice and left off Pettigrew's, so it is possible (though not likely) that Peter was in a different house (WBD).

When were they at Hogwarts?
1971-1972 - First year
1972-1973 - Second year
1973-1974 - Third year
1974-1975 - Fourth year
1975-1976 - Fifth year
1976-1977 - Sixth year
1977-1978 - Seventh year

Did they call themselves "the marauders?"
Yes, Jo confirmed this on her website (JKR).