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This supernatural slasher series benefits from the genre-establishing slasher films that came before it: the series began in 1984, when rival Friday the 13th was already four films in. Unlike its more mundane cousins, the supernatural element allowed the series to retain legitimate credibility as a horror franchise for far longer than one would otherwise expect, even after the inevitable descent into camp and self-awareness. The films, while of varying quality, average well above what Friday the 13th could consistently produce, and the series is far more dedicated to internal continuity than one might expect for films about a serial-killing nightmare bogeyman. Interestingly, in contrast to the Friday the 13th series (whose moral message is "avoid booze, pot, and premarital sex"), the Nightmare on Elm Street films mostly focus on children abandoned by their absent or dysfunctional parents.
A Nightmare on Elm Street (1984, 7.4)
The film drags a bit in the middle and feels like it's not quite fully fleshed out from an idea into a film. That said, it's quite watchable, much better than the first entry in the Friday the 13th series, and ends up being a fairly reasonable start for the series. The film ends up being the keystone on which the later films successfully build. Score: 3 stars out of 4.
A Nightmare on Elm Street 2: Freddy's Revenge (1985, 4.9)
Uh, wow, this one was out of left field. This one abandons everything built up by the previous movie, switches from nightmares to possession, and has a not-very-subtle, not-very-gay-friendly homoerotic subtext that ends up being more coherent than the textual plot of the film. It's not very surprising that later films refused to acknowledge that this film's plot ever happened... although a few of the later films grudgingly used scenes from it in their montages. Score: 0 stars out of 4, and my pity.
A Nightmare on Elm Street 3: Dream Warriors (1987, 6.3)
Easily the best film in the series. The film uses Nancy, protagonist of the first film and now an adult, to explicitly create continuity with the new cast (to great effect). It also successfully ratchets up the action by giving the protagonists more awareness of the situation, upping the stakes and giving the audience new hopes... to eventually dash, of course, when building up the climax. Score: 4 stars out of 4.
A Nightmare on Elm Street 4: The Dream Master (1988, 5.2)
This film felt like a "me too": it felt like it was trying too hard to emulate the secret sauce of the previous film. That said, it wasn't even remotely a bad film, and actually manages to be pretty decent. The ending even manages to approach "epic" territory. Score: 3 stars out of 4.
A Nightmare on Elm Street 5: The Dream Child (1989, 4.7)
A noticeable decline in the series, yet still enjoyable. The creative minds behind this film were obviously desperate for a plot to keep the cash cow mooing, with Freddy's backstory reaching new heights of camp, yet the result is far more watchable than it has any right to be. Score: 2 stars out of 4.
Freddy's Dead: The Final Nightmare (1991, 4.6)
Aaand the series dies. This film goes off the rails from the first scene onward, then proceeds to kill any seriousness left in the franchise and performs unspeakable acts on the corpse. It even has an obligatory sequence involving 3D glasses. But... it's still better than the second film. Score: 1 star out of 4.
Wes Craven's New Nightmare (1994, 6.3)
Ah, the meta-film, where the characters are themselves actors making a movie, but the inner movie breaks the fourth wall and becomes real. The film essentially re-creates the original film, going so far as to use many of the same cast members and have them play themselves in the present (i.e. 10 years later). It then re-does several of the kills from the original, but with a bigger effects budget and less camp. Because this was before the Scream franchise, the concept was actually quite fresh, and the result was actually quite good. The movie also stands well on its own; at most, you might want to see the original film so you can see the callbacks. Score: 4 stars out of 4.