The Ace: Forrest is this most of the time without even realizing it.
Accidental Athlete: Forrest ends up as a running back on Paul "Bear" Bryant's University of Alabama team when a couple of bullies chase him and he ends up running through the school field when the team was practicing. It helps when you consider exactly who he was seen by. For those of you unaware, Bryant is universally considered to be one of the greatest American football coaches of all time.
Accidental Hero: Of a sort. Forrest ran back into the combat zone to try finding Bubba, only to be called upon by other soldiers to rescue them, which he did by carrying them to the river. What he did was technically heroic but he didn't intend to save four others and be awarded the Medal of Honor. On the other hand, he did intend to save Bubba, and he was aware of the danger of the situation.
Achievements in Ignorance: Forrest is so dense that he routinely attempts things other people wouldn't even consider, and so single-minded that he puts his maximum effort into everything he does. As a result, he meets spectacular success while the skeptics are left scratching their heads.
Almighty Janitor: After his myriad accomplishments that leave him a war hero, shaper of history, and gazillionaire, Forrest accepts the prestigious job of groundskeeper at the University of Alabama, which he ends up doing for free because he likes it so much. Hey, at least he's keeping busy.
Super Speed: A mundane version, but a lot of Forrests' talents and accomplishments such as his football stardom, his super-fast gun-loading, his war heroism, and his uncanny talent for ping-pong, all come from being able to move and act extremely fast.
Vitriolic Best Buds: Forrest doesn't see it, but Lt. Dan has a lot of anger towards him and generally treats him with contempt. But underneath it is an appreciation that Forrest holds no grudges and will do anything to help a person in need. By the end, there is no doubt they are best friends.
Abusive Parents: In the words of Forrest, who didn't quite understand what was going on in the Curran household: "Her father was a very loving man. He was always kissing and touching her and her sisters..."
Animal Motifs: She's always associated with birds, from the moment she asks Forrest to pray with her.
Death by Adaptation: Jenny survives the original novel, although she is killed off at the beginning of the sequel novel, Gump and Co.
Driven to Suicide: The first time is after her nude guitar show when she is standing on a bridge and talking to Forrest about the time they prayed together. She is about to leap out of her shoes until slowly stepping back down. The second is when she's high on drugs and standing on an apartment balcony, ready to do a swan dive into the streets below... but comes to her senses at the last moment and climbs off the ledge.
Hate Sink: Invoked. Forrest was made nicer in the film, though some of his negative personality traits were given to Jenny, mostly to contrast their respectively simple, stable, and extravagant and dangerous lifestyles.
Death Seeker: He's had a family member die in every single war America has fought in, and thus feels it's his duty to do the same in Vietnam. He actually has a nervous breakdown after Forrest rescues him, because not only has he lost his legs, he doesn't know what to do now. He eventually gets better.
Disabled Snarker: Having no legs breaks his morale, but doesn't take away his sense of sarcasm.
Dropped a Bridge on Him: In the sequel novel, Gump and Co., when he gets killed by friendly fire during Operation Desert Storm.