This is quite an interesting question. Dickens's works do tend to adhere to moral codes of the time, so it would have been considered a happy ending for most that Bill Sikes, the criminal, dies at the end of the novel -- a fitting punishment for his treatment of Nancy -- and that Oliver's half-brother, Monks, is unmasked and dies in prison. Likewise, it is obviously a happy ending for Oliver himself, who inherits a considerable amount of money and is legally adopted by Mr. Brownlow, presumably living happily ever after.
However, Dickens also forces his readers to think about the "victim[s] of society," as the Artful Dodger calls himself. Jack Dodger is only a boy, but he has been forced into a life of pickpocketing and at the end of the story, he is deported to a penal colony in Australia. Dodger is by and large a sympathetic character, so this does not necessarily feel like a happy ending and might be considered rather excessive punishment. Likewise, Fagin is captured by the police and hanged. While Fagin has been a criminal for all of his adult life, he is a character with clear good points and the reader has come to be quite fond of him, in the same way as Fagin is obviously fond of the boys in his care, even though he exploits them.