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.
Crowning Moment of Funny: His performance of "Where It's At" on the show, Live at the Rehearsal Hall. It included cheap Casio keyboard that he told his keyboardist to switch to a different instrument voicing every so often, a Seinfeld-inspired "sitcom bass" solo, and other moments Beck described as "musical crimes." Even Beck couldn't help but crack up during the song.
Epic Riff: "E-Pro", and to a lesser extent, "Loser."
Signature Song: "Loser" is far and away his most popular song. "E-Pro" is easily in second place in the US, whereas "Where It's At" is elsewhere.
That little silly solo part in "Girl". Unlike the rest of the song, it sounds like a bunch of random notes played on untuned guitar.
Also, if we go by his initial idea, the lyrics to "Loser".
His vocal delivery on the verses of "Gamma Ray" is full of stuttering and hesitant pauses, as though he was either nervous or just struggling to remember the lyrics, while the chorus is sung much more confidently. Beck himself has said "I was trying to sound as bad as I could, for a laugh".
Various early songs, most notably "Trouble All My Days" (from Golden Feelings) and "Total Soul Future (Eat It)" (from Stereopathetic Soulmanure), have Beck detuning his guitar intentionally badly, to create bizarre and hilarious music.
Ear Worm: Many of the songs, especially the opening.
Koyuki and Shiingo pull this off a bit in England, where Koyuki waits for Maho to show up at Abbey Road for their big reunion in London, only for her not to show up. Cue the Rain. Then Shiingo shows up with an Umbrella of Togetherness...
Minor in-universe example with Koyuki and Matt Reed, of all people, where Matt flies Koyuki and Maho into the Avalon Festival in his helicopter... except that the gossip mags had said Matt would show up with his girlfriend. When Koyuki exits the chopper with Matt, several fans are quick to assume that Matt must swing both ways. "Just what I'd expect from a rock star!", indeed.
GET THE FUCK OUTTA HERE!!! (Ryusuke calling out on Koyuki, after the latter unintentionally breaks a guitar the former had given him in an early episode. Turns out that the guitar, which Ryusuke cherished for thinking it belonged to Eddie Lee, was a replica of Eddie's usual one, and all was good between them again.) It's only funny because of Ryusuke's accentized English.
Averted in the English dub, where the lack of an 'Engrish' accent helps the line's effectiveness.