Affectionate Nickname: Ms. Pac-Man is called "Pepper" by her husband. (Most likely, this was added because the lack of a first name would have been awkward. Pac-Man is called a variety of nicknames by other characters, like "Packy" and "Packster".)
Babysitting Episode: In "Hocus-Pocus Pac-Man", Ms. Pac-Man asks her husband to watch Pac-Baby while she goes shopping. Pac-Man tries to amuse Pac-Baby with some magic tricks, but one of them goes wrong and Pac-Baby seemingly vanishes.
Big Bad: Mezmaron is the only human in Pac-Man's world. He wants to take over the Power Forest, and the ghosts work for him. It's never explained what he plans to do with all those power pellets. As the lone recurring human character, he's our lone reference point for scale. Several episodes have Mezmaron mention that by taking over the Power Forest, he'll control all the "pac-power" in Pac-Land, and thus easily conquer the populace.
In "A Bad Case of the Chomps", Pac-Man shows Chomp-Chomp a wrench while dealing with a faulty bathroom sink, and says annoyed at him, "THIS IS A WRENCH."
In the second season premiere, the Ghost Monsters come after Pac Man with a tank armed with a "goo gun". Pinky tells Inky to load it; when Pinky asks "with what", Pinky replies, "with goo, what else?" while holding up a can of something labeled "Goo".
Clothing Damage: Mezmeron wasn't harmed by Pac-Man's chomping, but his clothes sure could be. Pretty much every plot that involved a face-to-face confrontation with Pac-Man ended with them ruined.
Conspicuous Gloves: Pac-Man, Ms. Pac-Man, Pac-Baby and Mezmaron all routinely wear gloves for no discernible reason. In "Backpackin' Packy", Pac-Man's gloves fail to protect him from a poisonous plant.
Criminal Doppelgänger: Pac-Man was once mistaken for a bank robber who escaped from prison. The fugitive managed to fool Ms. Pac-Man… until she read the newspaper a day late, and mistook her husband for the crook.
Did Not Do the Bloody Research: Ms. Pac-Man's affectionate nickname for Pac-Man, "Packy", is very unfortunately and hilariously pronounced the same way as a racist slur against people from Pakistan in the United Kingdom.
Face Palm: Mezmaron does this at the end of the season two opening.
Five-Bad Band: The ghost-monsters Inky, Blinky, Pinky, Clyde, and Sue.
Flintstone Theming: Most of the landmarks, characters, etc. in the show had the word "Pac" or "chomp" in their names; for example, Pac-land's movie capital was "Pac-Hollywood", and Pac-Man's dog was named "Chomp-Chomp".
Goldfish Poop Gang: The Ghost Monsters tend to act like this a lot, despite being the most visible antagonists.
Hoist by His Own Petard: Again, happened to the villains more often than not. The most overt example was when they tried to use a nightmare-inducing weapon on Pac-Man and ended up zapping themselves; the nightmares they experienced took up most of the episode. Also tended to happen to Sourpuss any time he tries to play jokes on Chomp-Chomp.
Limited Wardrobe: The ghost monsters were shown with a whole closet full of identical ghost suits to change into, after being chomped into floating eyes.
Dinky, the ghosts' nephew, needed Sue to help him get his spare suit when Pac-Baby chomped him.
In one episode, Mezmeron has to change outfits after Pac-Man ruins his robes (see Clothing Damage above) revealing that he has an entire wardrobe full of identical ones.
Mass "Oh, Crap!": The ghost monsters when Pac-Man eats a power pellet. "P-p-p-p-p-p-p-p-Pac Power!"
Later, when Super Pac-Man eats a super power pellet, Pac-Man realizes that as Super Pac-Man is a Nigh InvulnerableEating Machine who can't control his Super-Chomping, the only way to negate that and give Super Pac-Man some control again is to get him into his time-warp space hole. Fortunately, Pac-Man can grab it and use the hole to do just that.
Motor Mouth: Not in the H-B series, but in the Pac-Man record albums by Kid Stuff Records, Speedy (AKA: Pinky) talks this way.
Mythology Gag: "Neander-Pac-Man" had Pac-Man be chased by the ghost-monsters through a maze that was identical to the one in the original arcade game, and the episode "The Bionic Pac-Woman" began with Pac-Man and Pepper at an outdoor hamburger stand, ordering two Wakka-Wakka Burgers, referencing the sound made when Pac-Man ate dots in the original game.
Near Villain Victory: The episode "The Day the Forest Disappeared" had Mezmaron finally uproot the power forest, but Pac-Man defeated him at the last minute because the trees turned out to be sentient and Pac-Man told them to move to a new location where Mezmaron would never find them.
Never Say "Die": Chomping isn't eating. Chomping the ghosts turns them into floating eyes, just as in the game. Chomping Pac-Man or any other Pac-person (at least in earlier episodes) turns them into something resembling a sad bean bag chair, though they get better when fed power pellets.
Pity the Kidnapper: In "Pac-Baby Panic", when Mezmaron kidnaps Pac-Baby and tries to ransom him, this scenario happens quickly. When Pac-Man shows up to agree to Mezmaron's demands, the villain begs him to take his kid back.
Power-Up Food: The power pellets, of course. The second season added the "Super" power pellets for Super Pac-Man.
Punny Name: The Pac-Family's cat was named Sour Puss.
Sigil Spam: Expect the iconic "missing pizza slice" pac-shape to work its way into the design of the world. The sun, for example.
Spiritual Successor: Later games in the franchise take influence from this series. The game Pac-Man 2: The New Adventures seems at least partly based on this cartoon.
Stupid Evil: A lot of the villains' plans fall under this. For example, in the pilot, Pinky lifts the whole Yellow House (Pac-Land's version of the White House) by turning into a hot-air balloon while Pac Man, the President, and the other Ghost Monsters are inside, while Clyde threatens to tell Pinky to let go of it unless Pac-Man tells them where the Forest is. That's when Blinky realizes something... What would happen to them if Pinky did that? (Fortunately, Pac-Man is able to bluff them by leading them to a fake Power Forest.)
Surrounded by Idiots: Mezmeron was capable of inventing such things as a Time Machine, a rocket ship, and a machine that could turn a vampire bat into an actual vampire, but it was almost a certainty that his five minions would mess the plan up somehow.
Tertiary Sexual Characteristics: Ms. Pac-Man. One episode, "The Bionic Pac-Woman", even features Pac-Man disguising himself as Ms. Pac-Man to fool Mezmaron. Sue might fit this as well, being depicted with earrings and eyelashes, unlike the male ghost monsters (who wear hats).
Eye Beams: One time he fries Pinky off the bat with them: "Now you'll see why the girls in the galaxy say I have the hottest eyes in town!"
Trouser Space: Inky and Dinky (the ghosts' nephew) had this trait.
Voluntary Shape Shifting: Pinky all the time, but in "Picnic in Pac-Land", he could merge with Clyde, Blinky, and Inky to form items at times (once to a frisbee, then to a kite). Neither worked. The frisbee got buried by Chomp-Chomp and they had to exhume themselves, spitting out dirt. The kite got hit by lightning. In other episodes, the ghosts assumed such forms as traffic lights and hubcaps.
Your Costume Needs Work: In "The Greatest Show in Pacland", Pac-Man sees the ghost-monsters disguised as clowns and assumes them to be clowns dressed as the ghost-monsters. He proceeds to laugh and say that they look even dumber than the real ghost-monsters.