Wow. I'm in the minority here.
My answer is yes, it can be forgivable, and that depends very much on the person and circumstances. Sometimes, in really long term relationships where communication has broken down and the relationship has deteriorated, affairs happen. People always say, "well, if you're going to cheat, then you should fix your primary relationship or leave them!" Well, that's not simple at all. When you factor in things like finances, kids, living situations, and just basic human nature, you can rarely boil it down to something so simple. People aren't simple, and neither are relationships. Things that sound good when you say them, or like the moral highroad that we'd all like to take, are a different thing altogether when it comes to actually implementing them.
Relationships can come back from cheating, but it depends on the people involved and the circumstances---always . It also depends on how you go about repairing what has been damaged, because it usually takes a lot of patience, empathy, understanding, and a really good counselor. I think that cheating is often a symptom of a sick relationship, rarely the cause of what went wrong.
But for some people, it's a deal breaker, which is understandable. Trust is huge in a relationship, and once it's been violated, the person who has to try to trust again will often be haunted by what happened, insecure, and scared that they'll get hurt again once they let their guard down. Sometimes time heals wounds, and sometimes separation. Sometimes the damage is irreparable. There are just too many variables. But I still said yes, because I like to try to be an optimist...even though most things in life are not yes or no questions and depend on all kinds of things.