Badass: Particularly the way he handles 1955 Biff Tannen.
Berserk Button: "Nobody calls me chicken!" This ends up getting him into an accident the day he returns from 1885. (May also qualify as a Noodle Incident, since it didn't appear in the first movie. Though that may just be a coincidence.)
He also hates it when his friends or his mother are being abused.
Chekhov's Skill: Skateboarding, guitar shredding, and (later) arcade shooters.
Combat Pragmatist: Kind of necessary when facing guns and men twice your size (sometimes both at once).
Compressed Vice: Again, his dislike of being called a chicken. In the second movie, his parents reflect on how this was always his Fatal Flaw. Would be normal if it weren't for the fact that he doesn't have this trait in the first movie.
This Is Wrong on So Many Levels: Marty often reacts like this when stuff happens with his young mother and grandmother too in the game, for different reasons.
Tragic Hero: Narrowly subverted; his Fatal Flaw nearly causes him to break his hand and ruin his rock star dreams in a race with Needles or get shot by Buford, but he learns to overcome those flaws and therefore doesn't fall into tragedy.
True Companions: To Doc. In the movies, yes. But it's especially flagrant after the game.
Age Lift / Dawson Casting: Christopher Lloyd was only 48 when he filmed the role for the 71 year old Doc Brown. Probably done on purpose so when Marty goes back to 1955 and meets the 41 year old Doc Brown they look the same (except for aging make-up in 1985, which was dropped in the other parts as Brown underwent a rejuvenating process).
Hill Valley 1931 Science Expo. Young Emmett is driving his invention, a flying rocket powered car, which explodes. When Emmett is seen out of the expo, his hairs are like his movie counterpart, which he didn't have before. He comments that after when happened, he's banned from the expo for at least 50 years.
Intergenerational Friendship: It's a credit to the actors that we, as viewers, don't question why a skater punk and some old guy would hang out together.
The original script had a line by Marty explaining that Doc hired him to clean his garage. Marty, being a music aficionado, was impressed with Doc's vintage record collection. The rest is history.
The screenwriter decided it wasn't necessary to explain how they first met. Doc is a local pariah and a weirdo, and Marty is clearly a rebel. It's inevitable that Marty would snoop around Doc's garage at some point.
Literal-Minded: This comes up a couple of times in the first movie, where he takes Marty's use of slangnote "This is heavy at face value.
Meaningful Name: His first name is "Time", pronounced backwards. His ambition is to travel in time.
Older Than They Look: he's nearly one hundred years old in the game, yet still look like a man in his sixties. justified by the fact that he took advantage of future medicine to rejuvenate himself and increase his lifespan.
Omni Disciplinary Scientist: Aside from inventing a time machine with an on-board nuclear reactor, he's also managed to build a working refrigerator (well, it can produce ice, anyway) using 1885 components, and a second time machine that runs solely on steam power (again, using components available around 1885). Also, when he meets Clara and lets slip that he's a scientist, he mentions that he's a student of all sciences.
Took a Level in Badass: His first appearance in Part III involves him rescuing Marty from being hung by shooting the rope holding him up, then proceeds to get Buford and his goons to run off.
The Von Trope Family: In Part III Doc explains that his family use to be the "Von Brauns". He goes on to explain his father changed it to Brown because of World War One.
Word of Dante:invoked Bob Gale guesses that Doc was involved with the Manhattan project, but became an outcast and spent the remainder of his life trying to invent something beneficial for humanity. Hence the portable nuclear reactor which he sank his entire fortune into. This would also explain his cynical predictions for the future ("Of course! Because of all the fallout from the atomic wars!")
Playing Gertrude: Lea Thompson is just nine days older than Michael J. Fox. Though it does make perfect sense, as for most of the first film (intended as a one-shot story at the time) she's the same age as Marty.
George McFly (Crispin Glover, Jeffrey Weissman)
Adorkable: a nerd who is more comfortable watching or writing sci-fi than he is with social interaction and who takes notes on what to say to the girl he likes.
Berserk Button: When Biff pushes Lorraine to the ground, it prompts George to react with violence for probably the first time in his entire life.
Flashback with the Other Darrin: It may not be particularly noticeable most of the time due to clever camera work and tech, but the shots with George in Part II that aren't stock footage are played by Jeffrey Weissman.
The Southpaw: An early draft had George discover he could punch very strongly with his left hand. The final film has George's desire to protect Lorraine cause him to unleash his inner strength, but close observers might notice he knocked out Biff by punching him with his left hand.
Took a Level in Badass: Marty basically helps him rise to this point. As soon as Lorraine is shoved to the ground, the kid's gloves come off.
Biff Tannen (Thomas F. Wilson)
What are you looking at, butthead?!
Arch-Enemy: To the McFly Family in general, but mostly Marty in the first movie.
Berserk Button: He really hates Manure. When Marty told him he heard about the manure incident in 1985-A he seemed more angry than confused.
Egopolis: Alternate Hill Valley is a gigantic Shrine to Self. The front of his casino (formely the Clock Tower) is a museum dedicated to Biff's life, with a life-size wax statue and film reel describing his rapid rise to fortune.
In the alternate present, we see a headline describing George's murder; Biff, the actual gunman, crows that the police would never arrest him. The article explains that George was headed for a meeting to protest the environmental policies of Biffco.
Guest Star Party Member: Her most significant role was in the second film. Which involved her running around her future home in a controlled panic. The Bobs have noted that if they'd intended on making a sequel, they would not have had Jennifer go to the future with Marty and Doc as they had no idea what to do with her.
The Other Darrin: From Claudia Wells, to Elizabeth Shue, and back again. The opening scene of the second film is actually a painstakingly exact recreation of the end of the first, with the actress as the only difference.
Secret Keeper: She becomes this once Marty tells her about (and shows her whats left of) the Doc's time machine.
All There in the Manual: The novel says that Arthur went to WW 1 but was sent home when they noticed how young he was. Arthur returned home without even firing a single shot and became a laughing stock. This event destroyed his self-confidence.
Extreme Doormat: Like George, his future son, but overall, his life is less miserable than George's was.