Released in 1988, A Nightmare on Elm Street Part 4: The Dream Master was the start of the series' decline, with the movies becoming more comedic than horrifying. Adding Tuesday Knight to play Kristen (as the original actress was unable to appear for the film) and keeping both Joey (Rodney Eastman) and Kincaid (Ken Sagoes) as Freddy-fodder to tie it in with the previous film, the movie features some of the most (and least) graphic kills in the series.
Unlike A Nightmare on Elm Street Part 5: The Dream Child, this movie never got a pre-release without any censoring of violence, and is actually known to be missing at least one scene. Not only are the scenes in the screenplay, one also is partly shown in an early trailer and in some promotional shots.
Below is a rundown of the deleted scenes from the film.
NOTE: Some deletions were simple edits from other countries, some where deleted after the theatrical release, and others were not shown at all.
1) The best known deleted scene involves Kristen encountering Freddy for the first time in film. It would take place after Joey and Kincaid are killed, with Kristen falling asleep in her window while smoking. She wakes up in Freddy's house and ends up running down a long hall, with his clawed hand repeatedly stabbing through the wall after her. She then confronts Freddy and is nearly killed, being awoken by her cigarette burning her arm right before he can strike. It would then lead to her discovering the two missing at school the next day.
2) Also apparently filmed is a scene that takes place after Sheila dies, where Alice talks to her father in the kitchen only for it to be a dream.
3) During original screenings, when Freddy puts on his sunglasses a Miami Vice-like riff played. Due to possible copyright infringement with Jan Hammer, composer of the actual Miami Vice theme, the riff was removed and never restored.
4) In early VHS releases and the theatrical cut, the audio for Reefer Madness is intact. It was removed and only the piano can be heard in recent releases, but the lines still appear in the subtitles.
5) Until the 2001 restoration, 1 minutes and 7 seconds were cut from the movie in the UK. At first, only 56 seconds were removed, but more was removed for the home video release.
Back in 2011, an early trailer and a series of leaked stills of the scene with Freddy and Kristen had been posted on YouTube alongside the entirety of Freddy's Nightmares. However, sometime in 2012, all of this was deleted in some possible effort by New Line to deny the deleted scenes' existence.
The trailer had a scene with Freddy taunting Kristen, telling her '2 down, 1 to go'. Images from this scene were the most common, with a greenish lighting and Krueger standing amidst the chains. It looked similar to a later scene, since it was the same set, but there was a difference in the pose and angle of the shot.
There was also a glimpse of Kristen running down the hall with multiple hands bursting from the wall, but it was only about a second long. The quality of the trailer wasn't very good but the audio was in good shape, having slightly different narration.
The IMDB page dealing with alternate versions: 
A post with two images of removed scenes notice how the first cut scene is unmentioned but there is a still of it. There used to be a page about it with more images, but it has been deleted.