I would never think of becoming involved with another woman. I was married once before, and was faithful to her. As far as I know and can prove, she was physically faithful to me, but seemed to have no interest in being with me. My second marriage is much different than my first, and my wife and I are much closer to each other than we are to anyone else (children excluded). In my wife's first marriage, there was many trust issues, and the internet became a big issue, as her ex-husband got on the internet in a closed room and was involved in all sorts of activities. When my wife and I first got together, she noticed that I was on the computer a lot, but she also noticed that I was on my laptop right beside her, and she could see everything I was doing. I handled "heathen business" while she watched television. I have never hidden anything from her that I have done on the internet, and usually share things that are happening with her. She knows that I'm not flirting with other ladies online, looking at porn, or any other activity that would put our marriage in jeopardy. In fact, now that I'm in school, I am required to be on a computer more frequently, so I do spend more time away from the computer (not much, but some).
I have seen several people that call him/herself "Heathen" that is involved in Polygamy or Polyamory., or Polyandry. One cannot be faithful to more than one spouse at a time. If a man (or woman) is married and becomes involved with another woman (or man), the individual has broken trust and bonds with the spouse. The person has proven that he/she is not worthy of having that spouse, and it should stand that the person is not worthy of a future spouse. An unfaithful spouse is worthy of the same treatment as an oathbreaker, since when a couple gets married, there are oaths made in the marriage. Back before I came to being a Heathen, I believed in fidelity. I had been cheated on by girlfriends. I knew what it felt like, and did not want to be the cause of another person feeling that way.
When a marriage fails and children are involved, the children feel as if they need to take sides. I have seen this with my own daughters, and with my step-sons. They feel that their loyalty much be chosen, or that they have to split loyalty between the parents. This puts stress on the children when it comes time for them to make oaths and promises, and can contribute to the child failing to maintain fidelity on various levels.
Love your spouse and be faithful to him/her. Fulfill your oath that you made when you entered into marriage. If you are dating, do the same. I know some couples that are not legally married that are more faithful than those that are. A legal marriage isn't always important, but an oath to a significant other can be stronger than any document a government can grant. Marriage should not be a legal ceremony, but a spiritual connection formed between two people.