"The point is, the Quidditch Cup should have had our name on it these last two years."
-- Oliver Wood to the Gryffindor Quidditch Team (PA8)
This yearly competition is won by the Hogwarts House with the highest overall Quidditch score.
The trophy itself is "huge" and "silver" (PA8).
No Quidditch Cup was awarded for the 1992-93 school year (tournament cancelled due to concerns about Slytherin's monster) (CS14) or the 1994-95 school year (Triwizard Tournament took place instead) (GF12).
Where the Cup is kept is not clear. Ron Weasley says he had spent a lot of time polishing "that Quidditch cup" in the Trophy Room during his detention (CS7). However, Professor McGonagall states that she had "become accustomed to seeing the Quidditch Cup in my study", implying that the Cup is stored in the office of the head of the previous year's victorious House (OP19).