Ambiguous Gender/Ambiguously Gay: More like deliberately ambiguous in presentation, but not in conception. Since the children's books didn't establish Mei's gender, everyone at the time assumed it was a boy-meets-girl love story, and the story was well established as a romance for over a decade. But the 2005 film firmly established Mei as male, and the creator revealed that Mei was always intended to be male, but that ultimately his gender was not relevant to the story.
Break the Cutie: Mei's perfect faith and devotion to Gabu is never strongly challenged until near the end, when he is reunited with Gabu only to find out that Gabu had a Tap on the Head and has Identity Amnesia and cannot remember anything that happened, and that goat meat is and has always been Gabu's absolute favorite food. Mei has his only real loss of composure in his horror that the one he loves has forgotten him and wants to eat him as an indifferent stranger. But Gabu's memory is quickly jogged when Mei cries about the one stormy night together when they first met — their "Arashi no Yoru ni".
Carnivore Confusion: Gabu loves goat meat. Gabu loves Mei. Mei loves Gabu. Mei is willing to be eaten by Gabu if only one of them can live. Gabu has an emotional meltdown. This trope is used to subvert the Unresolved Sexual Tension trope.
Conspicuous CG: Some of the terrain stands out juuuuuust a bit. Not that it's any uglier for it.
Death Mountain: The impassable snow-covered mountain Mei and Gabu must pass to find their freedom.
Mei appears to die after he and Gabu fall over a waterfall. He lives.
After the avalanche, Mei thinks that Gabu has been killed. (He was originally intended to have died before the last book came out to Joss it, much in the same way that Sherlock Holmes was supposed to have died in FINA.) Gabu does turn out to be alive, but...
Does This Remind You of Anything?: The only brief time we see Mei getting mad is when he wakes up to Gabu sneaking back after having had a few snacks, to which Mei scolds him for doing it "every time when I sleep." note Sounds like a wife scolding her husband for eating midnight snacks or drinking behind her back.
Downer Beginning: It starts with Mei and his mother being attacked by wolves, to which Mei runs away while his mother stays behind to fight them, but ends up eaten.
Feuding Families: Wolves eat goats. Goats flee from wolves. They can never be friends.
Family-Unfriendly Violence: Not in Japan where the film was originally made and marketed. In the United States, it's probable parents might be uncomfortable letting their children see a movie where a goat rips off a wolf's ear with her teeth barely minutes in.
Gender Flip: The TV show apparently portrays Mei as a girl instead of a boy like in the film. The English dub even changes the spelling of the name to May.
Getting Crap Past the Radar: The way Beach's name is spelled in katakana (ビッチ, "bitchi") suggests it's actually meant to be rendered in English as Bitch (as "beach" would be more like "bichi"). Given the target audience, the different spelling in the translation is likely intentional.
Ghibli Hills: The idyllic Pleasant Mountain where Mei and his goat kin live. Also the Emerald Forest where Mei and Gabu are finally free to be together.
Go-Karting with Bowser: When Mei and Gabu's kin each learn that the two have been spending so much time together as friends, they are horrified and angered (respectively) at what they see as an ultimate blood betrayal.
Green Hill Zone: For the goats, every place away from Pleasant Mountain. It's beautiful, there's lots of food, and goats can be killed in broad daylight.
Happily Ever After: There are many people who believe that the book series concludes with Fubuki no Ashita, but this trope actually applies not only to the film, but the books as well.
Heroic Sacrifice: Averted twice. When Mei and Gabu are on their Death Mountain and slowly starving to death, Mei offers himself to be eaten by Gabu so that Gabu may live. Gabu, rejecting this, goes out to dig for grass to feed Mei, but confronts his wolf pack and decides Mei may be worth dying for, and attacks them. Gabu survives the fight and an avalanche, albeit with amnesia.
Identity Amnesia: After Gabu has a Tap on the Head (well, an avalanche), when he and Mei are next reunited, Gabu doesn't remember who he is or where he came from, except that goats are his absolute favorite food.
If It's You, It's Okay: Mei doesn't want to be eaten by a wolf or anyone, unless that wolf is his friend Gabu and there's no other choice.
Imagine Spot: Mei and Gabu finding out where each other lives and imagining what it must be like to be there.
Make Up or Break Up: With all their kin watching from afar, Mei and Gabu must either deceive each other or stay true to each other.
Meaningful Name: "Mei" is the Japanese onomatopoeia for the noise a goat makes and "gabu" is the one for biting.
Meadow Run: Mei runs happily across the meadow towards Gabu, but Gabu actually has Identity Amnesia and is running towards Mei to catch his prey.
Mistaken Identity: When Mei and Gabu first meet in the old barn, they can neither see each other nor smell each other, but they can talk to each other, and they become friends there. Only later does Mei realize that Gabu is a wolf (not another goat) and Gabu realizes that Mei is a goat (not another wolf). By this time, they have decided to be friends and they stay true to it.
Mordor: Gabu's home, Chomping Hills. At least if you're a goat. Or if you're a wolf who befriends goats.
The Mourning After: After Gabu's apparent death, a month passes by. But Mei is dejected to the point of feeling unable to keep on going without Gabu.
No Accounting for Taste: Mei looks very upset when he catches Gabu sneaking back after yet another night of catching and eating mice.
Parental Abandonment: Mei and Gabu's mothers have both already died. Gabu's father is mentioned once, but otherwise fathers are nowhere to be seen. Averted in the books, where Giro is Gabu's father.
Reasonable Authority Figure: The goat elder. And in abstract, his objection to Mei befriending a wolf is reasonable in context — if the wolf is not absolutely trustworthy to all the goats, it's a grim threat to their survival.
The Reveal: When Mei and Gabu meet for the second time, they see each other for the first time and realize they are different species. Eye-widening Body Language follows.
Suicidal Gotcha: Twice. First when Mei and Gabu suddenly decide to jump into the river together to be swept far away from the suspicious eyes of their kin. Then again when Mei and Gabu are fleeing their wolf pursuers in the forest and Gabu makes a brave leap he's never been able to make before.
Take a Third Option. Either act as The Mole for your kind, or have Mei be devoured by Gabu? Naaaaaah, just jump in the flash-flooded river!
Take My Hand: Gabu acts quickly to save Mei from being swept away by a fast-flowing river.
Was It All a Lie?: Suspected by Mei and Gabu's kin once their relationship is discovered that the other of the pair was The Mole to gather information about their enemies. Suspected briefly by Mei and Gabu themselves before being dismissed and proven wrong.
Yaoi Guys: Male Mei with Gabu in the film. But as his gender was previously always intentionally ambiguous, this only applies when his portrayal was very obviously male. This trope is not in full force in the storybook versions, as it's left for the audience to decide for themselves. And it's most definitely not in force for the CGI version, where Mei was specifically Gender Flipped to female.