The Fantastic Four's nemesis Doctor Doom cares not the first person! Of course, if you were named Victor Von Doom, you'd probably refer to yourself as "Doom" a lot too.
Minion: Doom, why does every word you say sound like you're speaking into a microphone? Doom: I am. Every word of Doom must be recorded for posterity.
The eponymous hero of Cerebus does this until the day he dies. And after. Though he has actually referred to himself as "I" at least once.
In the Astérix books, Julius Caesar would often do this. At one point he has the exchange "He's great!" "Who?" "Er... you!" "Oh, him!" This is a reference/parody to the fact that the real life Julius Caesar wrote his memoirs in third person.
Caliban of X-Men does this, at least in the early Morlock stories. Another Morlock, a one-shot named MeMe (whose name should be "good luck ever sleeping again") does this, too (with a Verbal Tic that has him repeating other words as well, so his name may actually be "Me").
Whether he uses his real name or his superhero name, Remy LeBeau (AKA: Gambit) occasionally falls into this.
In the Salvation arc of Preacherlocal villain Odin Quinncannon constantly refers to himself in the third person. Unfortunately for him, Jesse Custer hates people who do that and proves it by throwing Quincannon through the nearest window.
Rorschach of Watchmen sometimes uses the third person to refer to himself, but usually to distinguish between what he does and thinks as Rorschach and as Walter Kovacs, especially when describing his Freak Out.
The demon Etrigan tends to refer to himself by name a lot where there is a convenient rhyme to be made.
Petalwing, and presumably all of the Preservers in ElfQuest. They're also ignorant of pronouns, always referring to themselves by name.
In Kingdom, the only dog soldier who doesn't do this is Rex Horizon, to indicate his great intelligence.
Jack Kirby's Cosmic Dictator Darkseid has referred to himself in such a manner, often when giving speeches, though sometimes he does it in plain conversation.
The Spike, member of the second X-Force (before it was renamed X-Statix), often referred to himself as such. This is possibly an attempt to clarify that he bears no relation to team director Spike Freeman. Mr. Freeman's Spike; the Spike is ''the'' Spike, thank you.
The characters talk like this in the Malibu Mortal Kombat comics. You begin to wonder if Outworld lacks first person at all.
Rahan and other characters from the comic talk like this, being cavemen.
The Hulk often refers to himself in the third person. Depending on the Writer, this is either simply primitive Hulk Speak, the Hulk being arrogant ("Hulk is strongest one there is!") or a mixture of the two.
Mantis of The Avengers always referred to herself as "this one."
Sunfire: No need to thank me, Rio— thank the Avengers for having the foresight to beg Sunfire to join!
Vault, a minor villain from Invincible and its sister books The Astounding Wolf Man and Capes. Vault is a comically self-sure villain and an inveterate braggart, so it fits him very well. "Vault is prepared — unstoppable!"
In 2000 AD there is the Lowlife strip, featuring a wally squad (undercover) judge named Dirty Frank. He's pretty... odd... and generally refers to himself in the third person (and occasionally brushes against the fourth wall).