Boisterous Weakling: The only fight he's really "won" is against a very elderly cat who fell asleep while gumming him.
Cats Are Mean: Frequently abuses Satchel and Rob physically and verbally for no real reason at all, with his moments of kindness being few and far between. Several strips have noted that he was much more meek as a kitten.
Delusions of Eloquence: For example, he thinks "disinfect" means something like "bother".
Rob: I'm waiting for you to say something offensive. Bucky: Oh come on! Even I say we bonk ol' Svein on the head.
Hidden Depths: He's surprisingly good with machines, as demonstrated when he found and fixed Satchel's watch after it got broken by a bicycle courier. He even managed to make it run again, which it had stopped doing even before the accident.
Know-Nothing Know-It-All: Has a tendency to use words without knowing the definition, once describing himself as "highly intergalactic."
Rob: Now I know that's not what you meant, but it is, in fact, a true statement.
Strawman Political: He expresses far-right views, despite having little to no idea what he's talking about half the time, just to irritate his left-leaning owner, Rob.
Used to Be a Sweet Kid: Rob found him alone and scared in the trash as a kitten. There was a time where he was too afraid to even leave Satchel's side.
Rob: He used to be so cute... What the !@$# Happened? Satchel We may have been enablers...
Beware the Nice Ones: On the rare occasions he's lost his temper it's terrifying.
Camp Straight: He likes a lot of frilly, "feminine" things.
Character Development: He started out pretty much taking all of Bucky's abuse with barely a complaint but as time's gone on he's noticabley snarkier towards him and will actually stand up to Bucky.
"Well Done, Son" Guy: His dad isn't remotely happy that his son turned out to be a house pet.
Rob Wilco
Berserk Button: Don't say "Bucky Dent" around him, or mention the New York Yankees in general.
Important Haircut: Bucky accidentally putting some hair remover in his shampoo (Bucky meant it for himself) caused Rob to go bald for a while before growing his hair back shorter, soon after which he stopped wearing his Opaque Nerd Glasses.
No-Respect Guy: His pets don't even believe that he's the one who stocks the "magic cabinet" with food.
Only Sane Man: Rob's the one stuck dealing with all of Bucky and Satchel's idiosyncrasies.
Opaque Nerd Glasses: Early on in the strip's run. Later it's stated that he switched to contacts, but his glasses still show up from time to time.
Virtuous Vegetarianism: Despite eating meat products towards the beginning of the comic's run, Rob is a vegetarian on moral grounds. He has explained on more than one occasion that he doesn't eat meat because he finds the way animals are treated and butchered into food products to be too cruel. However, Rob's "virtue" mostly just serves to contrast with that of his cat Bucky, who wants to increase his meat intake just to spite Rob.
Silent Snarker: Never says a word, letting his expressions and the occasional sign do the talking for him.
Sitcom Arch-Nemesis: Towards Bucky. It started with Fungo glaring at a cowering Bucky during their first meeting, and they've had this relationship ever since.
Talking with Signs: During those times he needs to communicate with words.
Wicked Weasel: Subverted. He's neutral towards Rob and a good friend of Satchel, and only fights Bucky in retaliation.
Chubby Huggs
Badass Pacifist: He manages to stop a fight between Bucky and Fungo with a massive bear hug.
Cats Are Mean: Averted. One of the few in the strip that does so, to the point where he's actually one of the friendliest members of the cast.
Gentle Giant: From the perspectives of Bucky and Fungo when he wants to hug them, anyway.
Stout Strength: If he gives you a hug, you are very definitely getting a hug. He does 200 Hug-Ups and Buddy Crunches a day.
The Slacker: Considering just how long he's been secretly squatting in Rob's apartment...
The Unintelligible: At first, he was almost completely this trope, speaking in some sort of odd mish-mash of several British dialects. Later on, he became more understandable.
Buttercup
Badass Boast: Threatens to turn Bucky into Tender Vittles.
Big Eater: Gets 9 orders of pork from a take-out place. Justified as Rob's Mom had her on a vegetarian diet.
Vegetarian Carnivore: Invoked by Rob's Mom, though Buttercup isn't the least bit happy about it.
Foodar
Attention Deficit... Ooh, Shiny! Whenever even the slightest whiff of food is in the air, whatever conversation or activity he was doing beforehand gets put on hold until he finds it.
Threat Backfire: Twice. His attempt to blackmail Rob into paying Bucky's debt ended with Rob threatening to call animal control and the second with him threatening to kill Rob and Satchel only for Bucky to not care and actually encourage him.
Jerkass: His reaction to meeting his son for the first time in years is to berate him for being a housepet and say he's done nothing.
Mrs.Pooch
Generation Xerox: It's clear where her son got it from, as evidenced by her only onscreen actions being sticking up for Satchel and then giving him a big hug.