Some TMNT stuff was always meant for grownups.
In the original comics, Raphael was shown to be the most aggressive, tempered, violent, and competitive of the Ninja Turtles. You could almost call him a typical teenager, he often feels misunderstood and believes that he is alone in the world.
It is Raphael who is sent to issue a challenge to the Shredder by Splinter, and as he infiltrates Oroku Saki's security business, he kills several thugs. It is clear that he is the most aggressive. The Turtles return to their sewer home after the Shredder is killed.
When the Turtles rescue April O'Neil, who is an assistant to Mouser developer Baxter Stockman, it is Raphael who knocks him unconscious. After Stockman has the Mousers destroy his building, the Turtles return home to find destroyed Mousers and Splinter missing, April invites them back to her house.
In the earliest black-and-white Mirage Comics, Raphael was the most violent turtle and had a tendency for going berserk either in battle or when his temper flared up. His anger often brings out the worst in him, as one time he almost smashed Michelangelo's skull in a sparring match. His anger and stubbornness also causes him to repeatedly collide with Leonardo. He has a somewhat cynical and sarcastic sense of humor. In later issues, it's shown that he is not particularly fond of "Supernatural," stating it up front in Tales of Raphael: Bad Moon Rising.
Raphael mellowed somewhat as the series went on. Possibly a key moment for his character development was when he allowed Leonardo to go in alone to defeat the Shredder after nearly being killed by the Foot Elite in issue #21 of Volume 1. Since then, he has been less likely to challenge Leonardo's leadership, and on the whole is more friendly towards his family and allies.
Of his three brothers, Raphael is closest to Michelangelo, even having stated it in the fourth issue of the original TMNT comics. Raphael often shows a caring, more laid-back, side of himself when around his brother, even if he often annoys him, frequently indulging the younger turtle emotionally when at home and ferociously protecting him from harm when in battle. Raphael openly admits that the mere thought of his youngest brother being grievously injured causes him to experience violent rage. In his self-titled one-shot micro series, Raphael met human vigilante Casey Jones, his foil, who was even more violent and unstable than he was. Despite their brutal first meeting, the two have since formed a close bond and friendship.
In the comic book series' Volume 4, he is still the most violent turtle, but is more sociable. After having been bitten by a vampire-like creature in issue #12, he experienced a further mutation, and became a large, dinosaur-like version of himself. He went into a state of berserk animal rage because of it, but with some guidance by an inner manifestation of Master Splinter, he regained his original mentality and later assisted Leonardo and Casey Jones in tracking down the vampires who attacked him. This is also somewhat similar to an earlier storyline during Volume 1, where Raphael was attacked by a leech-like creature who, when sucking his blood, also drained him of the mutagen in his body and reverted him to a small turtle. The leech itself mutated and vanished, prompting the remaining turtles to follow it. Finally, after tracking down the creature, Raphael manages to bite it and pierce its skin, thereby drinking its blood and mutating back.
The Raph briefly appears in Trans-Dimensional Turtles.