The X-Men have had all manner of weird and not-quite human looking mutants fighting alongside of them. These have included the freakish looking Beak and Maggot, as well as the Morlock, Marrow. These individuals' appearances have typically made them stand out even among the X-Men, with fitting into human society essentially impossible.
Another X-Men connected character who is equally as strange looking is the innocuous Doop. Looking basically like a green potato, Doop's cartoony design fit right in with the unusually optimistic affairs of the X-Statix team. Despite how ridiculous he seems, he's actually got a connection to very prominent figures in the Marvel Universe.
The Origin of Doop
Doop's exact origins are rather mysterious, but it is known that he's in fact not a mutant. It was revealed by none other than Captain America that Doop was part of a Cold War experiment to create artificial life, resulting in the unorthodox looking creature. Doop apparently has a mother, though it's unknown if she actually gave birth to him in a "normal" fashion. His powers include superhuman strength, durability, flight and the power to store loads of items and even people inside of himself.
Doop can only learn and speak his own unique language, but it's just as well since everyone seems to be able to understand it anyways. His earliest adventures involve aiding in the fall of the Soviet Union, achieving his Cold War era goal. During this time he not only met Wolverine, but briefly became a private detective. Ironically, his investigative services would be hired to locate himself by a man who's wife Doop was previously having an affair with!
Joining X-Statix
The first official appearances of Doop would involve several silly yet somewhat tragic adventures. Here, he was a member of the mutant team X-Force, which had changed from its gritty '90s paramilitary roots into essentially a group of ditzy mutant celebrities. Doop was hired as their videographer, recording the footage of their exploits and battles. During one particular battle, almost all of the team dies save for Doop and a few others. They redub themselves X-Statix, diving even deeper into their roles as celebrities. This stark contrast from the darker themes of prejudice and oppression in the X-Men line made the zany Doop fit right in.
His wacky antics include going so far as to record the intimate activities of teammate El Guapo. He also later kills potential recruit Corkscrew by impaling him with an axe after mentally torturing him. This came after Doop had simply joked over Corkscrew killing an enemy, making both of their moralities incredibly suspect. At one point, his brain randomly exploded, forcing X-Statix and the Avengers to collect the various dispersed parts. Doop later developed a second brain, but this was right before what seemed to be the end for the character. Even after being restored to life with his brain, Doop and most of the rest of the team died after being shot down on their last mission together.
Schism and Krakoa
Doop would show up again later after crashing down from space. Polaris' referring to him as Daap made it somewhat ambiguous if this was in fact the true Doop, however. He would officially appear down the line by joining the staff of Wolverine's Jean Grey School for Higher Learning. In a call back to his meandering antics in the X-Statix days, many questioned why Doop was even there. This stemmed from his lazy, amoral personality, though he was in fact doing a lot of important work behind the scenes. This involved protecting the school from all external threats. This was showcased down the line when he protected several students after they had graduated.
Doop also became quite involved with several ladies, including Warbird of the Shi'ar Empire. He even developed feelings for Kitty Pryde, as portrayed in a mini-series written by Doop's creator Peter Milligan. Most recently, he's been shown to rejoin the X-Men as they've relocated to Krakoa, which is incredibly strange given his not being a mutant. It would seem that breaking all the rules is just part of the norm with Doop, however, making him the true outcast bad boy of Marvel's mutant teams.