Is Andy Dufresne innocent, or did he really murder his wife?
It's never conclusively proven, but it's highly likely that Andy is innocent. Halfway through the movie, we hear about Elmo Blatch confessing to a murder (to his cellmate) that accurately describes Andy's situation:
Tommy (Elmo's cellmate): Big twitchy fucker. Kind of roomie you pray you don't get. You know what I'm sayin'? 6 to 12 for armed burglary. Said he pulled hundreds of jobs...So one night like a joke, I say to him, I say, 'Yeah, Elmo? Who'd you kill?' So he says...
Elmo Blatch (flashback): I got me this job one time busin' tables at a country club. So I could case all these big rich pricks that come in. So I pick out this guy, go in one night and do his place. He wakes up and gives me shit. So I killed him. Him and this tasty bitch he was with. That's the best part. She's fucking this prick, see, this golf pro, but she's married to some other guy! Some hotshot banker. And he's the one they pinned it on.
It's not completely impossible that there is another banker's wife who's also cheating on her husband with a golf pro, and the husband ends up taking the fall for it even though he didn't do it. But it's highly (if not astronomically) unlikely for two accurately similar double murders to occur at roughly the same time, correctly describing all involved parties in such detail.
It's also technically possible that he's taking credit for a murder he did not commit, but the movie gives no indication that this would be the case.
It is fair to assume that Elmo's confession is genuine and refers to Andy's wife and lover, given the details he is correct about and general lack of evidence suggesting he's knowingly taking credit for something he didn't do.
The fact is, it is never explained in either the source novella or the movie whether or not Andy committed the murders, but at some point he stops trying to convince everyone that he's innocent. It is presumed that he's guilty, as at some point he has a discussion with Red who states, "Don't you know everyone in here is innocent?" That rhetorical question is meant to imply that everyone in Shawshank professes they are innocent, when in fact they're not.