Well, none.

The original music which which was written for the Harry Potter films (by John Williams, Nicholas Hooper and others), was tailored specifically to those movies — to enhance and uplift the drama. Removing that music would eradicate a major artistic component — and the films actually would not work dramatically without it. Preexisting songs could not effectively substitute for the scores. A, the lyrics would distract and get in the way of the drama, interfere with dialog, etc.; B, preexisting songs are not conceived and timed to work in tandem with the drama the way an original score is; C, mainstream pop/rock songs simply don’t suit the Harry Potter films aesthetically.

On rare occasions, popular songs can be used effectively — often in movies that take place in a past era, where tunes from that era can help evoke the time and place (as in the case of American Graffiti, Goodfellas, Casino, etc.) but that is the exception to the norm.

In most cases, when songs are littered throughout a movie’s various scenes, it is for business reasons. Movie studios have deals with record companies (and in many cases, the studio and record company are actually owned by the same conglomerate), by which a film will feature songs by popular artists, to lure fans of those artists to come see the film. Conversely, placing songs in a movie is an effective way of exposing audiences to the music, in hopes they will purchase the songs.

I should also point out that Harry Potter and the Goblet of Fire did actually contain two pop/rock songs, but one of them was “source music” (i.e. music which the characters on screen are listening to), and the other was played over the end credits (and not used as “dramatic” music in any actual scenes).