Genius Ditz: He and Butt-Head are incredibly stupid most of the time, but when they're commenting on music videos (and reality TV shows in the newer episodes) they can be surprisingly witty and clever with their comments.
Made of Iron: Seriously how is he still alive after everything He's been put through?
Because, as it says in the content warning, "Beavis and Butthead are not role models. They're not even human; they're cartoons. Some of the things they do would cause a person to get hurt, expelled, arrested, and possibly deported. To put it another way: Don't try this at home."
Pyromaniac: "FIRE! FIRE! FIRE!" It was toned down after that incident with the boy who set his trailer on fire and his mom blaming it on the show (despite that the family didn't have cable TV in their house), but when the show was revived in 2011, they brought it back.
The most popular Fanon name for him seems to be Buford.
Full Name Basis: It's not just his real name, it's his first and last names combined! One episode has another person asking Butt-head his name. He replies that it's "Butt". When the other character asks what his family name is, he replies "Head".
Characterization Marches On: Especially evident in the Marvel tie-in comics. She starts out as a more generic know-it-all but gains the wry, unflappable, sarcastic streak we all know and love later on.
Aesop Amnesia: He's repeatedly learned that Beavis and Butt-Head are crude, destructive morons (particularly notable in the episode where they "clean" his house), yet continues to rather naively support and encourage them. Though it's justified as Van Driessen has an optimism very uncharacteristic of the Highland High staff.
Characterization Marches On: Originally couldn't stand Beavis and Butthead and actually threatened to kill them in "Cleaning House". However, in later episodes, this gets toned down, as he starts to care about them and become more likeable and laidback in tone. He, in fact defends Beavis and Butthead during the time that they thought that the duo died. Something of which, he would never do in earlier episodes.
Abusive Parents: Mr. Stevenson has demonstrated that when confronted with an issue (such as the uncovering of his porno stack), he will essentially try to pin all the blame on Stewart. Not to mention how he was pretty willing to have Stewart get his ass kicked by Harry Sachs to save himself.