In episode 1, Yuma drops his deck on the ground, leading to this exchange between him and the cleaning robots:
Trashbot: Garbage! Garbage! Yuma: My deck is not garbage! Trashbot: Trash! Trash! Yuma: My deck is not trash! Trashbot: Shit! Shit! Shit! Yuma: You guys are doing this on purpose aren't you?!
Yuma saying his catchphrase underwater and nearly drowning.
In the dub of the second episode where Yuma meets Astral, the exchanges between him and Yuma are hilarious throughout pretty much the whole thing, from Yuma calling Astral "Captain Obvious" to Astral making his first observation (which is, basically, that Yuma is a really bad duelist). It ends with Astral saying, "I have a feeling that this is the beginning of a beautiful friendship—IF you do as I say."
In episode 5, the summoning of Baby Tiragon. There's this whole big, dramatic scene with crashing concrete and flying dust to herald the appearance of... a cute little kitten looking thing.
In episode 6, it's revealed that Tokunosuke scammed a kid by promising him a rare card if he could fill an entire room with dominoes. Kotori barges in and accidentally knocks them over, forcing him to restart. At the end of the episode, the kid is about to put in the last domino when he accidentally knocks them over.
In the dub version of episode 7, Yuma's reaction to the summoning of Galaxy Queen. His reaction and incredulous tone of voice make it funny:
Yuma: Dude, you just summoned your mom.
In episode 9, there's Yuma somehow not noticing he's wearing ridiculous clothes until the others point it out. Then when Yuma's Achacha Archer tries to attack Stray Cat, the cat turns around and reveals its demonic face. The archer gets terrified and quickly kills it.
Yuma duels his dad in a flashback. His dad tries to overlay Gagaga Magician and Gogogo Golem only to remember that he has no XYZ monsters. The image of Gogogo Golem collapsing on Gagaga Magician is hilarious. Like father like son.
Yuma desperately trying to apply for the World Duel Carnival in episode 26.
Yuma kicks Gauche in the nuts in episode 40, resulting in Gauche making what's one of the show's funniest faces.
As the battlefield around Yuma and III collapses, Takashi says it's just the AR. He takes off his D-Gazer and gives a massive Oh Crap face as it's clearly not the case. (Lucky this face was here; the scene isn't funny at all otherwise.)
In episode 80, everything that Alito does. The Imagine Spots, the bar scenes with Girag, the ways Yuma interrupts his attempts to get Kotori's attention, the music tracks, and his reaction to Yuma beating him are all glorious. (Note that this applies to the original - the dubbed version doesn't quite have the same effect.)
In Episode 78, Takashi stops Kotori and her friends for violating the school's dress code. Except that they're wearing the school's standard uniforms. The school's uniforms are against the school's dress code.
Whenever Gagaga Girl gets pouty for whatever reason (like Yuma having to abandon a duel in episode 81).
Also from episode 81, the sheer insanity of everyone dueling while doing something else at the same time, like skydiving, beach volleyball, tennis, ping pong, and wrestling. Talk about multitasking...
The scene straight after the OP theme in Episode 87. The opening scene was quite tense and dramatic, and therefore you'd expect the rest of the episode to follow suit; however, instead we jump to Yuma and Rei being chased to school by a pack of dogs due to Rei suggesting a shortcut.
Yuma's declaration that it's impossible for Rei to have attacked Alito, with the flawless logic of...
Yuma: It's because...because...because he sucks at everything!
Rei's method of "setting up a defense" during the duel...by Normal Summoning a 0 ATK monster. And his overblown reaction when he realizes what he's done is also rather amusing.
During episode 88, there is a rather stunning display of Yuma's incompetence with English words; he manages to mix up "Guardian" and "Cardigan", resulting in a rather amusing exchange.
Rei: I am a Barian's Guardian.
And not long after we find out what Rei actually is, he declares Yuma his "subordinate". He doesn't even let Yuma argue the matter, insisting on "subordinate" after Yuma asks why they can't be partners.
Several scenes with Shark and Rio (Episode 79 being a prime example during the scenes where they eat lunch and the end of the episode) give them rather funny interactions, usually with Rio calling Shark out on how bad of a brother he is. And Shark usually is not very happy about this, to say the least.
Gets even funnier in Episode 79 when Shark seemingly gets intimidated by Rio.
Episode 90. Afro!Yuma. Which occurred after Orbital 7 decided to fire an orbital satellite laser at Yuma.
Episode 92 involves a "Duel Monster Cafe," with Yuma and co. dressing up as various Duel Monsters. Most of them are fairly normal; Kotori as Gagaga Girl, Cathy as Cat Girl, and Yuma as Temtempo...then cut to Rei, stumbling awkwardly down the corridor dressed as Dandylion.◊
And then Anna busts down the wall to the cafe. Via cannon.
Episode 93 ends with Umimi encouraging Anna to pursue Yuma and shoving her toward him...knocking them both down a flight of stairs.
Episode 101 has Yuma being bounced around in the spaceship, and the borderline non-reaction/sarcastic comment from Shark.
Episode 103. Anything that has to do with muscular men in spandex. Also, Alito blowing up the entrance to a set of ruins using Blast with Chain cards.
Episode 105. Having proved himself quite the competent rock-climber as opposed to the less experienced Shark and Kaito, Yuma gets to the ruins...and he smells food. He starts walking towards it in a trance, and Shark initially thinks Yuma's sensed a Barian. Then he and Kaito realize what Yuma's doing. Their reaction is priceless, to say the least.
Girag's predicament in Episode 107. Getting stuck in a statue. You don't know half of what he's thinking because he can't even make facial expressions.
The first duel that Yuma fought in the WDC Carnival, which turned into a soccer match with everyone including the monsters and the spectators dressed up in uniforms and cheerleader outfits.
Episode 112 was pretty dark with Mr. Heartland's return...but then Semimaru shatters his statue, causing The Dragon to break down into tears and ruining the mood.
Yuma: Shut up, fly bastard!
Mr. Heartland: Flies are supposed to buzz and annoy people!
Pretty much the entirety of Episode 114 once IV arrives, with Kurage's silly-sounding slurring, and...
IV: Number 4, you say?! The number 4's MY thing! It's a special numeral! On top of that, Number 4 is a freaking jellyfish of all things!
Episode 122, in spite of all the terrible things that are happening. Mr. Heartland's silly behavior just absolutely ruins the mood...until...
Mr. Heartland: Just kidding.
In Episode 124, if you've ever watched Power Rangers, the Barian Emperor's introduction can be kinda hilarious, especially Vector's.
In Episode 144, Yuma is quietly building his deck. Anna comes bursting through the wall of his house on her cannon, knocking a tribal mask onto Yuma's face that he had hung on the wall. Anna apologizes, saying her cannon has bad brakes.
Episode 146, the look on Yuma's face when Kotori says she loves his smile.