The Heavy Weapons Guy of Team Fortress 2 carries a minigun weighing over three hundred pounds which costs $400,000 to fire for twelve seconds, and cackles insanely while using it. He's most likely to be the Boisterous Bruiser, but if his presence is bigger than his physical size, think how big his presence must be.
While not nearly as massive, the Soldier and Demoman also qualify, as Class-4s.
The Sly Cooper series has Murray; the team's strongman and getaway driver. He was more a burden than anything else in the first game, but really came into his own in the second and third games, wherein he was shown single-handedly knocking the stuffing out of entire armies of mooks, all while Chewing the Scenery like no one else.
The others even occasionally call him "Big Guy."
Dekao from Rockman.EXE (known as Dex in the American dub).
His appearence in Mario & Luigi: Bowser's Inside Story is a solid Class 4, shouting about most everything while boasting stats that are almost double the M-Bros' at a lower level. Though it's understandable because he's by himself out there.
Brick from Borderlands is this trope to a Class 1 Berserker tee. In the second game, he's more a Class 4.
Borderlands 2 has Salvador and Krieg, who are both Class 4. Both are openly psychotic in their own way, with Krieg in particular being so insane that he seems incapable of talking in anything but nonsense.
Halo: Reach's Noble Team heavy weapons trooper Jorge-052. As an older Spartan-II, Jorge is the physically largest Spartan in Noble team standing at 7'4, 320 pounds. He's a Type-2, a Gentle Giant who is markedly more stable than most of his team-mates and has a wide sentimental streak.
It should be pointed out that, thanks to their bio-modifications (such as skeletal grafts) and their Powered Armor (those who have it, anyway), all Spartans can count as this. It's just that, compared to Elites, Brutes, and Hunters, they're average at best.
Kimahri from Final Fantasy X is good example of this, being a Ronso and holding off Seymour Natus on the Bevelle Highbridge while Yuna and co. escape.
If not him, then Auron. Tall, quiet, undeniably badass and whose natural stat growth has the most strength boosts out of all of them. He wields a sword bigger than himself and doesn't flinch when Behemoths are staring him down.
Fran in Final Fantasy XII. Obviously the most noticeable, being a Viera, and thus having bunny ears, tends to go on berserker rages, and also literally as she towers over the rest of the party(even without the ears). In regular combat, Basch serves as the big guy, having the highest strength until Vaan catches up at extremely high levels, as well as the highest HP. Having the lowest vitality ironically makes him the best tank when combined with his high HP.
In Final Fantasy VIII, Zell and Selphie both fit this role, while also both occasionally becoming The Smart Guy, for different reasons. Zell is the muscled brawler and Selphie is the best with weaponry and explosives.
Zaalbar and Hanharr from the Knights of the Old Republic series. Zaalbar is a quiet, shy fellow who lets Mission do the talking. (She even describes him as a "Big ol' softie") Definitely a Class 2; piss him off (or threaten Mission), and he will carve you up. Hanharr is recruit-able only by Dark Side Exiles, and is an Ax-CrazyOmnicidal Maniac who you gain influence with by ridiculing - definitely Class 1. Both of them are utter damage sponges, especially if you equip them with vibroblades.
Also by Bioware is Jade Empire with Black Whirlwind. He is an unrepentant Class 4 who just shrugs with a "Meh" whenever he's told his most recent story is the dumbest thing ever told. While an effective fighter, he is far more memorable for his many colorful and incredibly violent stories.
You actually get to control him at one point to hold off an army.
Each different colour of Pikmin have different attributes in terms of strengths and weakness. The purple ones, being ten times as strong and heavy as those of any other colour, quite clearly slot into 'Big Guy' status.
Eddie Riggs from Brütal Legend could be Class 5. A big guy, who is smart enough to put together cars in seconds (albeit easily made cars) and supposedly able to fix anything, and build anything. In many ways he fulfills the roles of The Big Guy, The Smart Guy and The Lancer, seeing himself mostly as the Roadie to Lars' front-man.
The Breath of Fire series include one of these among the chosen heroes: Ox in I, Rand in II, Garr in III and Cray in IV.
In Dragon Age: Origins, Sten serves as a Class 3, being a solid stoic who nonetheless has a definite soft side (enjoys art, kittens and has a Sweet Tooth). Oghren is a Class 4, a seemingly perpetually drunken Boisterous Bruiser. Shale is a cross between a Class 4 and Class 1, she lives only to crush her enemies' heads and watch the blood fountain. And to destroy all pigeons.
In Dragon Age II, Fenris takes this role despite being a scrawny elf. A scrawny elf that has Lyrium laced through his entire body and specializes in BFSes, that is. Whether he proves to be a Class 3 or a Class 1 mostly depends on whether Hawke pursues a friendship or a rivalry with him.
Aveline also fills this role, being the heavily armoured, sword and board guardswoman who acts as the protector and tank of the group. She is likely a Class 3, because she talks tough, but is also the Team Mom.
Dragon Age: Inquisition has the Iron Bull, who is explicitly called "The Muscle" in promo material. He's a heavily scarred Qunari mercenary, but he's really a Boisterous Bruiser whose priorities are protecting the innocent and having fun. Cassandra may also qualify, as she's a sword-and-board type whose Shield Bash can act as a battering ram.
Mass Effect 1, Wrex falls neatly into class 1, although some of his dialogue hints that he may originally have been a class 5. In the sequel, the Tank-Grown krogan Grunt is a class IV while the ruthless mercenary Zaeed is a Class I, with Jack serving as a Dark Action Girl example.
If Wrex survives, he becomes a clean Class 5 in the sequel. When you find him, he's on the way to re-uniting his people, a feat no one would ever believe possible.
Not only re-uniting, but doing so in a way which itself should be impossible from what we've heard of the krogan race - he's taken the ever-so-important krogan traditions that have been around for longer than the human race has been civilized, beaten them until they can't stand. At least if you believe his opponents and detractors.
Those very same Krogan traditions would enthusiastically agree with that approach. Beating things senseless is what the Krogan are there for.
Mass Effect 3 has James Vega: he's easily the beefiest human character thus far, and is built more around survivability than other characters. There's a reason he shares two of his powers with Grunt. Whenever you find him in the Normandy's shuttle bay, he's usually shown to be doing pull-ups in his down time.
Ashley is a female Class 4. She's a little hotheaded, protective of her team-mates and specializes in damage output.
Sweetwater in Battlefield: Bad Company is a Class 5 Genius Bruiser/Smart Guy and a rare "not larger than the others" version. As the squad's SAW gunner, he does carry a larger weapon, and he's not afraid to use it. When a Russian soldier surprises him by running up to the roof just as the squad is hopping off their Blackhawk and onto it, Sweetwater, without breaking stride, hits the poor bastard clear off the roof with his SAW.
Walter in the Mental Series is larger than the other two characters, and as such can do things the others can't, such as pushing obstacles out of the way and lifting heavy objects.
Rhino from War Frame. He is the heaviest Warframe and stands taller than any other frame except Saryn, and his Primed variant features some serious Shoulders of Doom. He is built to fill the tank role in the group, both via his CC abilities and his enormous armor, health, and shield reserves. Aforementioned traits also allow him to use the heaviest weapons in the game without fear of making himself an easy target, since he can easily soak up the gunfire while dishing out immense damage in return.