I'm someone who's forgiven a brief affair many years ago and contrary to what others think would happen to them/say did happen to them, I love my husband more than I did before it happened.
In terms of the effect on children, ours know about the affair and have learnt some amazing lessons about the importance of fidelity and the value of forgiveness.
For my husband, this provided a real wake-up call that although we'd always had a strong marriage, he'd been really quite selfish all his life. I had always known that, but his other qualities had made up for it; his kindness, his humour and his love for me and the children.
The post-affair period of individual counselling made him address certain ingrained personality flaws in a way he never would have, if not for that catalyst. My therapy gave me permission to be less tolerant of things I'd been making bargains with (e.g kind vs. selfish) and gave me the opportunity to hold out for what I felt I was worth.
The transformation in him as a person, husband and father has been astonishing. I wouldn't trade him now for the pre-affair model and neither would I trade our current relationship for what we have now.
As for me, I've gone from strength to strength. It's very hard not to take an affair personally, but a combination of my counselling, reading and most of all my husband's honesty helped me to realise that the affair wasn't actually about me, or even our relationship in the sense that it hadn't been an escape from difficulties within it. Some aspects of our relationship though had made the conditions for an affair more likely e.g. my acceptance of the aforementioned selfishness and neither of us realising the link between selfishness and affairs.
Like the other poster, I actually like myself much more now and my marriage is more grown-up, honest and mutually supportive than it was before. Also, seeing a man in his forties change incredibly ingrained habits and face his own demons has enhanced my respect and love for him. It's not easy to make such fundamental change to oneself, but only the potential loss of everything he held dear would have provided the motivation. As for my husband, he likes himself much more now too.
I'm not one of those people who says the affair was the best thing that ever happened, because patently it was not. It's one of the most gut-wrenching, painful things a couple and individuals can withstand. But it doesn't have to be the worst thing either and with enough determination, love and honesty, some enormous good can occur in its wake. We both feel much better prepared now to help our children face their own relationship dilemmas and because we've been very honest with them about our crisis, they have a far more realistic view of relationships and the challenges they sometimes provide.