Being a hardcore Nightmare and Friday fan, I'm about to give the complete history on both characters and the films.
CONTAINS MAJOR SPOILERS
Freddy Kreuger: Freddy Kreuger was the offspring of a gang rape to his mother. The son of a hundred thousand bastard maniacs. He had a tormented childhood full of being made fun of, and his father used to abuse him. One day his father tried to abuse him, and Fred just took it and smiled, and proceed to kill him. Freddy got married and had a daughter. A theory based on Freddys Nightmares has Freddy being an Ice Cream Man, using that as a lure to kidnap kids and kill them. He got caught, went to jail, and his lawyer got him off at the trial. Somewhere in here they take away his daughter. So the parents take it in their own hands to burn him alive, and they do. But wait, the dream demons are in luck cause they've found the most sadistic guy in the world, perfect for the job of killing people in their dreams. They offer Fred the power, he accepts, and boom, you got Freddy Kreuger. His motive is that he wants to hurt the children of the parents who burned him. Later his big motive is explained to be that he wants to make them pay for taking away his daughter.
NOES 1- You have to imagine that Freddy is new on the job, so he's not in one liner mode yet. He's just getting comfortable, and taking his new found power more seriously. In this movie, Fred kills a couple teenagers who have sex, and than finds his first real nemesis in Nancy. Nancy figures out the source of Freddys Power, and realizes that all you have to do is bring him out of the dream into the real word, and than he's human. So she does, but things go wrong. Some ancient book says that demons back in the day got their power from fear, and that if you stopped believing in them, they'll go away. She does that with Freddy, who dissapears. The next morning she's about to go to school when some weird shit happens and Freddy kills her mother. A theory on this is that the whole movie was just a dream by Nancy, sort of like a big premonition, and the very end is the only real thing that happened. Who knows though.
NEO2- This movie sucks. It's a couple of years later, and a new kid moves into Nancys old house. He finds her diary, reads about her troubles, and than some weird shit begins to happen. Freddy has some elaborate plan to get into this kids body and use it to kill in the outside world. The plot is stupid though, and doesn't fit in with the rest of the series. Not to mention the lead character is very gay. The ending is cool though, as Freddy reveals that he's still ticking.
NEO3- The 2nd best in the series behind the first. Kids who have been having trouble with a certain killer are all in a hospital full of doctors who can't figure out whats happening. They figure the only way to cure the kids is to make them go to sleep and face their dreams. The kids are called dream warriors, which happens to be the name of the movie. This movie intoduces the plot that someone call pull another person into their dreams. This is the same hospital from FVJ, so it ties in pretty well. Freddy has killed a bunch of teens at this point, and is really starting to love his job. Instead of taking things serious, he does elaborate dream sequences to kill his victims. He also reveals one of the greatest one liners in the series "Welcome to Primetime bitch". He's still dark and evil, just having fun now. This movie marks the return of Nancy, who comes to the hospital to help, and her father from the first one. Somehow they figure if they bury the bones of Freddy, he'll just die. So they do it, and hey, they think he dies. The kids are all decent actors, including Patricia Arquette, and Lawrence Fisbourn has a small role. Good overall movie, and Nancy bites the bullet in the end.
NOES 4- The Dream master stars the 3 survivors from the last one, but they're all killed off in the first 15 minutes, bummer. Freddy is ressurected when a dog pisses on his grave...you read that right. Freddy, absolutely loving his job now, plays with his victoms. He knows his true invincibility, and knows he can't be beat, so he conjures up more elaborate dream sequences to kill his prey. One particalar funny sequences is with this guy who's into Karate, Freddy takes care of him good. Freddys mom appears in this one also, as she did in part 3, giving tips to the heroin and so forth. The lead character is now Alice, and someway or another, Freddy bites the bullet in the end again. Not as good as 3, but good non the less.
NOES 5- This movie sucks too. Alice returns, pregnant. Problem is, she keeps seeing her child in her dreams. Freddy has become friends with her child in her dreams, who is named Jacob. Jacob in the dreams trust Freddy, and Freddy treats him like a little brother. In full comedy mode, Freddy kills Alice new friends in true comic book ways. Another funny ass one liner is when he makes this bulemic chick eat all this food until she explodes. He than says "Bon Appetite Bitch"! At the end, Jacob turns on Freddy, goes with his mother. And Freds mother tries to get rid of Freddy for good only to have Freddy burst from her stomache.
NOES 6- All the kids in Elm Street have been wiped out, so it would seem Freddys job is done. He's gotten his revenge, and now he can just go away....but Freddy has other plans. Theirs actually one survivor left on Elm Street. An unnamed guy, who in the original script, is actually Jacob from the 5th one. So Jacob is the only teenager left, and he has amnesia. A shelter some place else finds him and a girl tries to help him figure out his past. They go back to Elm Street, with a couple of troubled kids hiding in the back. The kids, being the smart ones, find a house on Elm Street to stay in while the girl and Jacob got try to find Jacobs roots. This movie makes no attempts at horror, Freddy is the hero now, he spits one liners left and right, and laughs hysterically at the way he disposes of his victims. If you love funny Freddy, this is the movie for you. He kills Jacob, right before thanking him for bringing him his daughter! It all comes full circle as Freddy finds out that his daughter is the only person who can bring him what he wants. As Freddy says "Every town has an Elm Street"! He now has the abilities to make an Elm Street wherever he wants, and kill whatever teenagers he wants. At first, it was all about revenge, but Freddy loves killing teens so much that he can't stop. Freddys daughter brings him into the real world ala Nancy, and blows him up with Dynamite. At this point, the Dream Demons temporary leave Freddy who ends up in his own Hell. This leads into Freddy pulling down Jasons mask in Jason Goes to hell.
New Nightmare: Not a member of the rest of the series. You have to ignore it for FVJ to make sense. Now all that was off the top of my head, but I can tell you I'm a much bigger Jason fan. I'll do my F13th write up in a little while, and THAT will tell you everything in the history of Jason Vorhees.