These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Angst? What Angst?: Beeza and her species in "The Ball" had to constantly move from planet to planet to escape from Buster, who practically destroys not only the planet but all the hard work they had done in it. Sure, they treat it as routine, but it gets worse when she mentions that they have no planets left and they will just keep flying until they run out of fuel or food, whichever comes first.
Awesome Ego: Lord Hater definitely, but to a lesser extent, Emperor Awesome fits this by trope and even more so by trope name.
Base Breaker: Wander, the lead protagonist, has become this. Many fans love him and find his antics entertaining and fun, but others find him incredibly annoying and uninteresting compared to Lord Hater.
Bizarro Episode: "The Void", in which Wander and Sylvia visit a white space (think Michael Crichton's Sphere) where anything either of them dream up comes immediately true, and the rules of logic and common sense do not apply. It's pretty much non-stop insanity from start to finish.
Fanon: Wander's species is called a "star nomad." As of this writing, we've never seen any indication that Wander has a species. McCracken did call Wander "nomadic" and there's a star on his hat, but he's never been referred to this in canon.
Ho Yay: In the Title Sequence, Wander hugs a perplexed Lord Hater while a heart appears behind them. Could also count as Foe Yay, on Hater's side (since Wander doesn't seem to consider him an enemy in any way).
There's also quite a bit of kissing between the Bingleborps in "The Greatest".
In "The Birthday Boy" Wander is all too eager to kiss Hater in a game of Spin the Bottle.
In one of the scenarios in "The Brainstorm," Hater winds up married to Wander, who hugs him while emitting cartoon hearts (though admittedly, this only happens in Hater's mind).
The biggest one is at the end of "The Rider" Hater shouts that he hates Wander, while Wander says that he loves Hater back.
The way Peepers acts towards Hater, especially in "The Buddies", it wouldn't be farfetched to assume there's a bit of a Bodyguard Crush going on there.
Inferred Holocaust: While we don't see an owner in "The Ball", Buster does have a dog tag with his name on it. So Beeza and her people have a new home until Buster's owner (or someone else) finds him and decides to give him a bath/flea dip.
Memetic Mutation: From "The Picnic", Wander carefully scooting down the side of the crater.
Lord Hater is a reaction face gold mine.
Wander taking selfies.
It's quite common on Tumblr for fans to take clips from the show (that involve notable movement) and sync them up to popular songs or pieces of music. Usually the first shot of Wander in the opening, where he's walking with changing backgrounds. This meme even resulted in an official Wander over Yonder promo set to Quest to the Hall of the Mountain King
Private Westley from 'The Little Guy' is extremely popular despite only being in one episode (aside from one cameo in the first season finale.)
Beeza from 'The Ball'
The two-headed fruit bartender from 'The Bad Guy' has a ton of fanart, moreso than any of the other characters in that episode.
The BLACK CUBE from 'The Fancy Party'. It's eerie floating and pseudo-Latin gibberish (as well as the fact that the whole area distorts when it speaks) makes it give off the feeling of being an Eldritch Abomination, making it one of the most memorable of the villains at the party.
Visual Effects of Awesome: The opening sequence, showing off the sheer variety to every character and world introduced in the show, repeatedly cycling through different backdrops and aliens- each of which feels different to the last. It's a real testament to the creativity and imagination behind the show.