The Real Man is the Tabletop RPG player who plays the game for the visceral, action-packed experience. Any character played by this guy will invariably be a Bad Ass whirlwind of death — rarely do they play any sort of sneaky or supporting character. If by chance they have to play a wizard, he'll either be loaded to the gills with fireballs or decidedly non-squishy. The real man may do some Min-Maxing (though not to the insane heights of the Munchkin), but he's just as likely to select abilities based on "cool factor"alone.
These players are most interested in the parts of the game that involve fighting. Their strategies tend to be simple; run up to the enemies and hack them to bits (or blast them with the big guns in a modern setting). However, the more imaginative among them may employ some killer stunts, such as shield-surfing or swinging on chandeliers. Unlike The Loonie (whose stunts are played for laughs), this guy is doing it purely for the Rule Of Cool.
The real man is handy to have around when a fight breaks out. He'll support his teammates when it counts (unlike the Munchkin who typically looks out for number one), and usually has a grasp on basic combat tactics. However, he's not as adept in situations where violence is not the answer. While some 'real men' are also skilled roleplayers (who just happen to enjoy a good brawl), others tend to stay silent when it's time for talking, relying mostly on well-worn archetypes (the trenchcoatedstoic, for example), rather than the more original characters of the typical Roleplayer.
Then there are more problematic forms of The Real Man:
The Leeroy: The guy with no patience for long-term strategy, deliberations, or diplomacy. He usually has one tried-and-true solution to every problem: the headlong charge. This may even work, on occasion, depending on how strong the Leeroy is. However, more often it leads to him getting in over his head (and even getting the entire party killed trying to bail him out) or getting mauled by a trap. Even worse is if he gets bored and starts a Bar Brawl during delicate negotiations because it's been more than ten minutes since the last fight. Named after the most famous recent example, Leeroy Jenkins.
Gourry Gabriev from Slayers, the only non-mage in the core cast, and something of a Leeroy Jenkins, as his only available tactic when facing the assorted sorcerers, demon lords and humanoid abominations that they're typically pitted against is a straightforward charge with his Infinity+1 Sword.
D&D's 4th edition seems to be built to easily accommodate this kind of player. Mechanics favor the "awesomeness" in moves present above, with very little squishy or loner character traits. Near to a middle ground between the other archetypes.
However, it also regulates it by more carefully standardizing the damage each class can do at each level. The class descriptions even give advice for min/maxing since they've taken steps to (in theory) ensure you can't take it too far.
For some people, the mechanics of DnD 4e make it hard to enjoy oneself while "Real Manning". Instant gibs have been pretty much restricted to minions, and there's nothing awesome in killing a One Hit Point Wonder in one hit. It would be much more fun if everyone was easier to kill.
There are some classes and builds that can dish out so much pain in such a short time that even Boss enemies can fall or at least become serioulsy crippled within one turn. A two-weapon Ranger using Blade Cascade (even the errataed version) with a few build-ups beforehand can easily instagib most lieutenant level mobs, and with a bit of luck rolling the dice sometimes even bosses. The major disadvantage is that this only works once a day, so it'd best be saved for that one big enemy.
In large part the appeal of Exalted, an RPG that specializes in being over-the-top awesome, that will actually let you jump 100 feet in the air, while whirling two blades around you to parry a hail of incoming arrows, then land head-first on the bad guy to smash him literally into the ground.
Paranoia and Toon also largely work on the Rule Of Cool, in that awesome ideas, even if highly impractical, literally have a better chance of working than boring ideas. Of course, both are liable to get your character smashed into a pulp on a regular basis, but what isn't?
It's an actual rule in Paranoia that characters are not allowed to change their actions after declaring them unless the GM thinks it would be funny, as in "Oh, Moe-O-DJO is going to detonate his solar grenade? Shoot, forget about diving for cover, I'm going to strip off my armor so I get a tan!"*
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Any RPG that uses Wuxia-type mechanics, such as Feng Shui or Wushu.
To elaborate on Wushu: while it's not entirely clear from the above statement what "wuxia-type mechanics" would actually be, the system does at its very core reward players for stunting (in that the more details they provide, the more dice they get to roll, at least up to a GM-determined "cap") and also throws in the "Principle of Narrative Truth", i.e. any statement by a player about what happens in the game that doesn't get vetoed by another player or the GM becomes fact (although by the rules this obviously can't be used to short-circuit an ongoing conflict before its "proper" mechanical resolution). Which allows the Real Men to directly mechanically benefit from providing blow-by-blow descriptions of their character's awesomeness.
Scion actively encourages this kind of play with the Stunting mechanic that gives bonus dice and refreshes Legend based on how cool it is from a scale of 1, nifty and adds depth to the action, to 3, leaves everyone around the table speechless at the sheer amount of awesome involved in the action.
Similarly, Changeling The Lost has Stunting in Dream-Fighting (similar to Scion's Stunting; +1 for cool idea, +2 for cool idea with lush description, +3 for idea that inspires applause and exultation from the table).
a Big Guns optimized character have little choice but to be this. Not only the stats required for Big Guns already provide the Required Secondary Powers for Big Guns (damage resistance and carry weight for instance, due to them being, well, heavy), as well as Big Guns penalizing Sneak. This makes Big Guns character a primarily a charging character that relies on tough defense (and a healthy dose of Stimpaks hotkeyed) and the guns doing the killing before the character gets killed.
Guns are for wimps! All melee with tons of Strength and Endurance is where it's at. Prepare to spend a lot of time sprinting towards your targets, laughing as you either soak the bullets or dash around cover, all for the glorious VATS teleport kills.
Legolas from DM of the Rings. When the players learn that the success of the entire campaign comes down to the die roll of a single NPC, Aragorn and Gimli are understandably upset, but Legolas thinks it's hardcore. He's also the player who comes up with all the crazy stunts and who never, ever grows tired of shooting orcs in the face.
V, despite being quite possibly not a man at all (it's deliberately ambiguous what V's sex is), is the wizard variety. V once used a spell called "Familicide" to ensure that he would never have to deal with some dragon's relations, no matter how distant, coming to look for vengeance. He estimated that as a result the world's population of black dragons decreased by approximately 25%.
Vriska from Homestuck is one of these, playing a pirate character based metatextually on Captain Hook who has 'gained all the levels. All of them.' This leads her to butt heads with her RP partner, who is The Roleplayer and plays a class that's useless but fits his personality best. The main thing keeping her from falling fully into Munchkin territory is that her character, while a God Mode Sue, still represents her various interests and fannish obsessions. She's been known to roleplay as her character outside of mechanics-based games as well, although apparently she 'only does horrible things as her'.
Cory of One Piece: Grand Line 3 Point 5 is both this and a Munchkin, who pimped out Zoro to an insane degree in order to maximize his killing ability. He's extremely frustrated when the GM bars him from playing his character at first, instead sticking him with the pre-made Coby.
Friendship is Dragons has Rainbow Dash, whose player repeatedly complains about the lack of awesome action and the setting in general.