Teen Titans Go! has been largely eschewed by purists as the annoying kid sibling of the superior Teen Titans cartoon, and met with outrage for its continued airing years after Teen Titans was canceled.
While I sympathize with the plight of Titans fans, I must admit my allegiance: I adore TTG. It's funny, it's weird, and I love a show that dunks on Robin near-constantly. I believe there is room enough for all manner of Teen Titans in this world, and if you've never experienced TTG, here's a guide to the episodes that should help you determine if it's for you.
Season 1, Episode 7, "Girls Night Out"
When Cyborg, Robin, and Beast Boy have a boys' night out filled with manly activities (trying on hats, primarily), Starfire feels left out of the gender-based socialization. So she takes a reluctant Raven and breaks Jinx out of prison for a girls' night of delicate and ladylike female bonding (police chases, destruction of a building, breaking out of prison again).
Season 1, Episode 25, "Colors of Raven"
When the Titans have trouble determining what Raven is thinking due to her lackluster, dry sensibilities, they split her into five distinct personalities — Happiness, Passion, Timidity, Rage, and Laziness. Not only is this a fun episode about all the pieces that create a complicated personality, but it's a tour de force from the iconic Tara Strong, who voices Raven and her Emoticlones.
Season 2, Episode 32, "Let's Get Serious"
A direct response to those who deride TTG for not being as serious as TT, "Let's Get Serious" serves as a reminder that the two are different beasts entirely — and this beast is silly. The best part is easily Starfire who's sole purpose in the "serious" form is to almost declare her love to a focused Robin (as opposed to his irritating crush to her complete disinterest).
Season 3, Episode 10, "40, 40, 20'
Not only is this episode, as well as the four-parter that would follow the next season, a triumph of '80s-style animation, but the song "The Night Begins to Shine" is an effing banger, totally deserving of five full episodes to literally sing its praises.
Season 4, Episode 50, "Bro-pocalypse"
Episodes involving Raven and Starfire teaming up are always favorites of mine, and this one where they relentlessly mock bro culture is no exception. Leaving the boys behind (they're all injured from trying to become the Ultimate Bro), Starfire and Raven search deep within themselves, pop their collars and learn the real Ultimate Bro was the friends they made along the way (themselves, specifically). Any episode where men — especially our own heroes — are the butt of the joke is a winner.
Season 4, Episode 7, "BBSFBDAY!"
When Beast Boy learns that Starfire doesn't have an Earth birthday, he offers to share his with her. It goes poorly. Very honestly, this episode isn't important or special necessarily. It's just really funny and it features Beast Boy and Starfire dancing a lot like this and that's worth the price of admission.