The musical sung by the background characters in "The Extras". Not only it is the first time many of these characters were treated as anything beyond a Living Prop, they also take over the show and have awesome voices, especially The Green Bear.
"I'm On My Way", a delightful little tune that plays at various parts in "The Origins", and is used as the background music for Darwin's song in Part 2. It also shows Darwin's long journey from the seashore to Elmore, which ended with him horribly hurt, but he never gave up.
"The Amazing World of Elmore", from Season 2 episode "The World", is sung by various objects in Elmore, with fun and creative lyrics. It also helps that many of them are from previous episodes.
"What He Thinks About Us" from "The Words". He literally tells his classmates what he really thinks of them in the form of song. That's both awesome and funny!
Also from the same episode, "No More Mister Nice Guy". He shows a scary musical number about how he will always be honest.
Tobias's and Gumball's song about surviving the weekend on the school roof. It helps that the backing track is as close to "I'll Make A Man Out Of You" in Mulan as they could get without pissing off Disney.
"Elmore Help Desk" from "The Butterfly", a hilarious and surprisingly catchy song that gradually escalates into chaos, all the while Karen tries to juggle between five different customers calling for service.
Darwin has one awesome rock ballad in "The Matchmaker", in which he sings about his love for Carrie. For a ten-year-old, he's got some impressive pipes. It helps that it's clearly based on "Without You I'm Nothing" by Placebo.
Richard sings about his love of fried food in I Prefer All My Food Fried most passionately. And as an added bonus, it's in the style of "Always On My Mind" by Willie Nelson.
"Goodbye" from "The Uncle", where Gumball ends his friendship with Ocho via a Black Comedy-laden R&B ballad showing his anger issues and what he could do to get rid of him, including but not limited to repossessing his house, getting him arrested for grand theft auto, shipping him off to Uruguay/Qatar/Somewhere-stan, or turning him into doner kebab. It is one of the few songs with an available instrumental, which is also very catchy.
"Books are Violent" from "The Blame", in which Gumball and his friends argue that books are just as violent as video games. Going through numerous classic works of fiction from Shakespeare to Mark Twain, it's impressive how they form the argument going from song to rap, as chaotic as it gets at times. Of course by the end, the parents they're presenting this argument to comically miss the point of it all.
Gumball and Darwin's "Make the Most Of It" rap is a classic. It's the perfect amount of Insane Troll Logic and Fridge Logic rolled into one song. The imagination they have during this song is just plain radical. You can't say you've ever daydreamed of being a ninja dentist, or a wizard cop with wings. Can you?
"I Can Sing" from "The Boredom" begins with a Serendipitous Symphony of car alarms, followed by a sad tune of Sal explaining he once wanted to be a musician, and ending with a bouncy and lighthearted tune where he apologizes to everyone he stole from. It turns out Sal is not a good singer at all and the good singing was all in his head, but at least he created a surprisingly catchy and whimsical song to go with it!
"Life Ain't Perfect" from "The Faith" has Gumball and Darwin sing to Alan to restore his faith in the world. And it worked!
A Shout-Out and In-Universe example in "The Console", a battle theme that mirrors Final Fantasy VII's iconic battle theme plays many times through the episode. At one point, Anais, Gumball and Darwin decide to stop for a little bit just to listen the song and sing along.
In the end of "The Parents", after Nicole's parents leave the house without reconciling with their daughter, Gumball sings "If It's Too Hard to Forgive", a song about their broken relationship. They start leaving in their car, but Daniel Senicourt changes his mind and drives back for him and his wife to hug his daughter. It was actually about the Christmas presents they owe him, though.
"Out of Sync" from "The Silence", sung by Gumball and Darwin when they think they're getting bored of each other. Even with them being out of sync, as the title implies, it's still pretty good.
"A Sorcerer's Apprentice" from "The Sorcerer", a totally rocking glam rock tune complete with fancy guitar licks and blasting synthesizers...and it's about doing chores for an old witch.
"All Hail All Hallow's Eve" from "The Ghouls" is such a delightful theme for what's arguably one of the best holidays of the year. All of the Elmore residents sing about their love for Halloween with more or less some solid Fridge Logic about the Holiday, from the art of trick or treating and scoring tons of candy to how retail workers and businesses make tons of money from the holiday. Nearly everyone is wearing a costume akin to pop culture, and it's not hard to tell that the cast and crew had lots of fun with this tune.
Heck, even the background music of the show’s occasional "serious" episodes is a step-up from the usual soundtrack. Examples include "The Void”, "The Shell", "The Future" and "The Inquisition".
, from "The Compilation". Sweet Dreams Fuel incarnate, even if the creepy clown from "The Procrastinators" and "The Saint", Gargaroth from "The Scam", and the twitchy pig scientist who injected Gumball and Darwin with serum that turned them into fungal mutants are in it.