I have felt that closeness. In some cases you can just be grateful for that closeness and companionship. Sometimes it can be a stopgap or sounding board to help you work on your marriage or current relationship.
If you would ever consider a real affair here's a site where you can find a lot of input from those who have been or are in affairs and how it has affected their lives. They will give you guidlines on how to set bounderies or warnings and reasons for not embarking on that kind of relationship.
http://messageboards.ivillage.com/iv-rlmyaffair
Whatever you do the fact that you have considered an affair is usually a sign that something is missing from your marriage. Think long and hard about what that is and see if you can't change things. On the other hand if you aren't married and the other person is I would suggest trying to find that closeness with someone else. They will never be able to give you what you need in a relationship if they are currently attached.
Good Luck
__________________
"Always learn the rules so that you can break them properly." Dalai Lama
My Karma just ran over your Dogma.