If you're asking yourself that question, then somewhere within you there must be a desire to forgive the other person.
After all, if you knew 100% for sure without doubts that you definitely should NOT forgive, then you wouldn't be entertaining the question, right?
You would have already said your goodbyes and would be moving on with your new life and licking your wounds. You may or may not have trust issues in your future relationships depending on how you processed the infidelity in your past.
But what if you are struggling with the question? What then?
The first thing you need to look at above and beyond all else is the cheater's character.
Do they have a history of cheating on their partners? Do they have a history of cheating on you?
Are they too self-centered to deny themselves whatever pleasures come along? Are they well meaning but weak?
Unless someone's incredibly ugly, they're going to face temptation some time during their life.
Saying no is all about having backbone, willpower, self-discipline, and the ability to truly care about another person's feelings.
Does your partner have all of those traits? If not, then forget it. Move on.
Let's assume for whatever reason that you have decided that yes your partner has the ability to be faithful and this was a one time indiscretion.
You now need to look at why they did what they did.
Motivation is more important than the act itself. If you know why they cheated, then it's possible to avoid having the same triggers repeated.
Were you emotionally and physically distant for so long that you may as well have pushed them into finding love elsewhere?
We are a love hungry species. Our spirits die when we do not feel loved. The body will follow.
You've heard of the old couples who die within a short time of each other.
You've also seen the studies they've done with the baby monkeys who don't thrive and grow without their mamas. It's the way of us to seek love.
That's our supreme motivator. So look at the causes of infidelity. If you can honestly say that yes you were completely loving and supportive and they cheated anyway, then you may want to consider walking away from them.
If they give you some other reason that makes absolute sense to you and you can truly see it as a forgivable reason, then so be it.
Forgive them. If they don't have a reason that makes sense to you, then don't forgive them.
The next thing to evaluate is what is at stake. What kind of a life have you built together and what does it mean to you? Do you have children together? A long marriage?