Brave Fencer Musashi gives us Ben, Ed, and Topo of the Leader's Force who serve Colonel Capricciola. A running gag with them is that they each believe they are the leader of the group and, at every available opportunity, remind the other two of it.
Castlevania III: Dracula's Curse had the Terrible Trio, which were the Stage 7 bosses (the first two you may or may not have fought yet). You had to fight Twin mummies, a Cyclops and the Leviathan all in one sitting. If you died, you'd have to start over from the first of the Terrible Trio.
Does previous example even count? They're just 3 bosses in a single battle, but they're not comedic elements nor incompetent henchmen or something like that.
Chrono Cross: Karsh, Zoah, and Marcy would be a more competent Terrible Trio, while Solt, Peppor, and Ketchop would be the bumbling trio. Granted, Ketchop is only seen if you recruit Pierre, but he's the closest thing they've got.
The Striped Brigands in Final Fantasy: Crystal Chronicles. Their leader, Bal Dat, is pretty cruel to his counterparts Artemecion (a moogle) and Meh Gat (an old man who eventually dies), but they're completely harmless.
The Terrible Trio of the Archadian Empire in Final Fantasy XII, although technically one of them isn't from the Empire.
The Chebukki siblings in Final Fantasy XI: Chains of Promathia. However, the sole female, Cherukiki, is notably not the leader. Rather, the elder brother, Makki-Chebukki, acts as one.
Conchita, Felix, and Bruce from God Hand. Naturally, they're Expies of the Skull Trio. Eventually, they're taken out not by Gene, but by The Rival Azel.
The Trump from Gunbird and the Queen Pirates from Gunbird 2. The latter are Skull Trio Expies.
Pink, Kain, and Kotaro in Gunstar Heroes and the remake/sequel Gunstar Super Heroes. Interestingly, they seem to be based on Grandis' gang from Nadia: The Secret of Blue Water, which in turn are a homage to the Time Bokan franchise's villainous trios.
Marluxia, Larxene and Axel could count, although they are actually extremely competant and dangerous, and one of them isn't quite whathe appears...
They are also directly rivaled by another such trio: Zexion, Lexaeus and Vexen.
The Heavenly Kings of Orochi in The King of Fighters. Consists of Chris, Yashiro, and Shermie, with their "boss" being Orochi himself (and to a lesser extent, Goenitz).
The Legendary Starfy's group of Ronk, Papes and Snips is called "The Terrible Trio". The characters are quite visibly done by an artist other than the series's main one, given how much their character designs clash with the other characters, most obviously Snips, the leader.
In a more minor example, in The Legend of Zelda: The Wind Waker, the miniboss of the Wind Temple is a Red Wizzrobe who at the beginning of the battle summons a Darknut and a Wizzrobe, so the miniboss battle starts off with a Terrible Trio. The two Wizzrobes will summon more enemies if given the chance, however.
Violen (short and fat), Agile (tall and skinny) and Serges (leader) from Mega Man X2.
Mitsumete Knight has the Burston brothers. The youngest, Billy, is the domineering one of sorts due to being the most agressive of the three and the most antagonizing with the Asian (the player avatar) ; Sam is the brainy one and Jack the big brawly dumb one.
Kabal, Kobra and Kira in Mortal Kombat, well Mortal Kombat Deception (onwards) anyway. Kabal the leader of the newely reformed Black Dragon clan, Kobra and Kira as the two henchmen (one male and one female, to keep up with the opposite henchmen ideal), terrible in the sense that they're Chaotic Evil. Kabal himself is nowhere 'near' being the Big Bad. In fact, the entire goal of the clan he now commands is to rebel against the ideals that the current Big Bad has.
Strega of Persona 3 are a trio of antagonistic Persona users who the team fights on occasion consisting of Takaya, Jin and Chidori. They're just an annoyance to the heroes in the grand scheme of things, (though Takaya is responsible for killing Shinjiro) nor do they usually put up a particularly impressive fight (though in your case you always outnumber them in a fight especially since they never fight you together). Later on however, Chidori performs a High-Heel–Face Turn for the sake of Junpei, though she's eventually killed by Takaya.
The heroes of Sly Cooper are like this — Sly, Bentley and Murray.
Solatorobo seems to have one as an enemy team compete with a pushy female boss.
It's predecessor, Tail Concerto also featured the Black Cat Gang in a much more prominent role.
Sonic Heroes has its entire gameplay point set in the Terrible Trio trope. But the best example is Team Chaotix, with the oversized and extremely loud leader Vector, the slim and calm Espio, and the hyperactive Charmy Bee.
Granted Team Chaotix are more self serving protagonists than villains.
Dr "Eggman" Robotnik and his two henchbots, Orbot and Cubot play this more straight in Sonic Colors (this setup is actually much akin to that used in Adventures of Sonic the Hedgehog (see below) and Sonic X (see above)).
Odie and his henchmen in Soul Nomad & the World Eaters borders this and the Goldfish Poop Gang. Storywise they are an incompetent gang of bandits (Odie the leader, with the farmer and the two beasts as the henchies), but they do show they're not so bad, Odie can join the party and show he's not such an incompetent magician after all...
Super Magnetic Neo has the Pinki Gang, which comprises of Pinki (the female leader), Yasu (the nerdy, smart guy) and Gasu (the big, dumb brute). Although, in this case, the said female leader is a baby.
The Three Mischievous Fairies in Touhou, with Sunny Milk as the leader, Luna Child as the dutiful subordinate, and Star Sapphire as the only one intelligent enough to flee whenever they annoy one of the more powerful denizens of Gensoukyou (i.e. anyone).
Stinky Pete, Gunslinger, and Blacksmith in the final level of the Toy Story 2 video game, all three of whom where fought individually as mini-bosses in previous levels.
Since the campaign mode of Transformers: War for Cybertron features a team of three playable characters for each mission, the three available characters for each mission in the Decepticon campaign could qualify as this. In the first mission, you have Megatron (the leader), Barricade (the brains), and Brawl (the muscle). In the second mission, you have the three Seekers, Starscream (the leader), Thundercracker (the brains), and Skywarp (the muscle). For the remaining missions, you have Megatron (the leader), Soundwave (the brains), and Breakdown (the muscle).
Bordeoux, Negimaru and Grein from the .hack//G.U. Games trilogy were a trio of fairly skilled and ruthless PKs under the command of Master Gabi, until Bordeoux's unhealthy obssession with Haseo caused the team to fall apart.