Benny, from the Axis of Awesome. Their intro overlooks him, and many of their sketches (The Glorious Epic of Three Men being the only one that comes immediately to mind) place him in the role of the helpless victim in some way.
Most celebrities are butt monkeys of the famous rapper Eminem's jokes in his songs (Kim Kardashian, Dr. Dre, etc.)
Nick "Peanut" Baines, the keyboardist of Kaiser Chiefs, is the Butt Monkey of the band. Just look at what the singer said about him on his Wikipedia page; "He likes to go the front and clap, and while he was at the front clapping, we all went off. Left him there on his own."
Jorma Taccone of The Lonely Island comes off as one. This is most notable in "I'm on a Boat", where Andy chooses T-Pain to go on the boat with him and Kiv, rather than Jorma. The rest of the video is filled with shots of Jorm suffering or doing mundane things while the others are out having fun.
Ian Casselman from Marianas Trench constantly has jokes made at his expense. According to him, the nicest thing that singer Josh Ramsay ever said to him was that he was like Jar Jar Binks.
Jason Newsted, former bassist of Metallica, was the Butt Monkey of the band the entire time he was a part of them. He was always the target of the band's pranks, his bass playing was almost completely mixed out of ...And Justice For All, and he was hated by the majority of the fanbase simply because he wasn't Cliff. Luckily Rob Trujillo, Jason's replacement, hasn't received much of this treatment.
In Paramore, the band seem to really enjoy making jokes at Hayley's expense. In an unknown amount of clips, if one is being embarrassed or teased, its probably her. Possibly due to her status as the Band's face, possibly on account of being the smallest, or possibly being the only girl. Either way, they really enjoy locking her out of the stage door and threatening to kill her on camera.
John Frusciante was also treated somewhat badly by Anthony Kiedis during his first tenure with the band, but it wasn't obvious to Kiedis because Frusciante's public persona was so hyperactive. Perhaps out of apology, when Frusciante rejoined the band he effectively became the leader.
Ruben Valtierra, who handles keyboard duties for "Weird Al" Yankovic while on tour. In part because he's been with Al's band the least amount of time (which is still twenty years at this point), and in part because he does the least on the albums themselves (usually backup keyboards, with Al handling main duties), he gets mocked frequently on tour, humiliated as part of between-song skits, and teased reguarly on Al's website. He didn't get to appear on an album's liner notes at all until Running With Scissors... and was then shown face-down with scissors sticking out of his back. His first non-humiliating appearance in the liner notes is 2011's Alpocalypse.