Peter Pettigrew, also known as Wormtail (nickname derived from his animagus form), was a good friend of James, Sirius, and Lupin. He was also secret-keeper for James and Lily when they were forced to go into hiding from Lord Voldemort, but betrayed them to save himself, resulting in the fulfillment of the prophecy.
Pettigrew was also described in DH in one of Snape's memories to be quieter than the rest of the group.
In his youth, he [Pettigrew] latched onto James Potter and Sirius Black, more talented and popular students, idolizing them and living vicariously through their accomplishments, as well as joining them in bullying other students, such as Severus Snape, whom he would not have been likely to cross without James and Sirius to back him up. Due to the huge difference in terms of talent, bravery, and popularity, Peter was more of a hanger-on than an actual equal.
(Harry Potter Wiki)
Pettigrew was very useful to the Marauders because he, in his animagus form of a rat, was able to paralyse the Whomping Willow to open the tunnel to the Shrieking Shack (x) where they would all go when Lupin transformed under the full moon.
No canonical evidence shows that the other Marauders particularly disliked Pettigrew, but similarly there is no evidence showing they liked him very much. One could easily infer that the group only kept him around because of his use when Lupin transformed. According to McGonagall, he wasn't a very competent student, but he does seem advanced in the Dark Arts:
Despite Professor McGonagall claiming that Pettigrew was a barely competent student, and Voldemort later denoting him as a poor wizard, he showed a surprising amount of capability in certain situations. From what is known, Peter does not seem to be any less magically capable than the other three Marauders. In fact, he seems to be quite adept at using the Dark Arts; perhaps even the most capable of all four.
(source)
Perhaps that was the only reason the Marauders kept him around; perhaps it was Peter's idea in the first place to become Animagi when they didn't want to leave Lupin behind die to his situation, and perhaps Peter was the one who did all the research and taught them all how to transform.
There are countless possibilities as to why the Marauders accepted Pettigrew, because he did not at all seem popular in the books except for the fact that he was friends with James Potter, Sirius Black, and Remus Lupin.
