"Doomguy" is the name given by fans to the anonymous space marine that the player controls throughout every game in the Doom series. Next to nothing is known about him specifically, apart from the incident that got his ass to Mars: he not only refused to follow a direct order to fire on innocent civilians, he put the officer who gave that order in a full-body cast. He couldn't exactly be court martialed for this, as the order in question was totally illegal, so he was "promoted" to a position in the least interesting post in the entire military: guarding the scientists and eggheads studying the ancient ruins on Mars.
As it turned out, this quickly became the most exciting post in the solar system, as the scientists accidentally opened a portal to Hell while experimenting with the alien technology, releasing hundreds of murderous demons throughout the facilities. In general, the marine grits his teeth while shooting Hell's denizens, and when not actively shooting, is constantly on the look for more ammo and health. He seems to enjoy using weapons, as he shows a completely badass grin whenever he picks up a new one. He has a pet rabbit, Daisy, who he left behind on Earth when he was shipped to Mars. Tragically, this bunny was killed by the invading demon hordes at some point before the end of the last episode of Doom, "Inferno". However, he got revenge by killing most of the demons that invaded Earth in the expansion episode, "Thy Flesh Consumed" of The Ultimate Doom, not to mention the sequel, Doom Il: Hell on Earth.
This character also makes an appearance in Quake III: Arena and its online browser based port Quake Live, under the imaginative name 'Doom'.
"Doomguy" has no officially recognized name. Chapter text breaks in Doom and Doom II address the player directly as Doomguy ("YOU'VE NEVER HEARD OF ANYONE ESCAPING FROM HELL, BUT YOU'LL MAKE THE BASTARDS SORRY THEY EVER HEARD OF YOU!" etc.) In Doom 3, in-game characters never refer to the player character by name, only calling him 'marine'.
In the Doom series of novels by Dafydd ab Hugh and Brad Linaweaver, Doomguy is given the name Corporal Flynn "Fly" Taggart. This does not officially extend to the game universe though.
It is also suggested that Doomguy is a descendant of B.J. Blazkowicz, and is another continuation of that line (Commander Keen is acknowledged as B.J.'s grandson). However, his is never directly stated or implied within any of the Doom games.
He is seen dead and dismembered in Duke Nukem 3D. Duke Nukem says upon finding his corpse "Hmm, that's one doomed space marine".