Oliver has almost no friends for most of his life. When he gets to London, he meets The Artful Dodger, Jack Dawkins. Dodger is not exactly a friend, although he does bring Oliver to Fagin. Oliver certainly sees Dodger as a friend, because he is too naive to understand that Dodger is taking advantage of him.
Oliver befriends Nancy, even though Fagin and Sikes make fun of her for it. She is a prostitute, and "a fine one for a child to make a friend of" but she stands up for Oliver, looks out for him, and eventually gives her life for him. Nancy knows that Oliver does not have the temperament or background befitting a life of crime, and she does all she can to return him to his rightful social standing.
Brownlow and Rose Maylie can both also be considered friends of Oliver. They are both his benefactors, and they take him in and trust him. Despite Oliver’s apparent bad situation and misdeeds, they both see him for who he is and realize his innocence and good character.