This is becoming a common problem and is a serious problem for many. A few months ago, I was upset after discovering online sexual cyber chatting, phone calls, and even a planned rendezvous. Like your spouse, my spouse also claimed she was not cheating. However, when a person pretends to be single and develops an online relationship with words of attraction and sexual flirtation, the feelings of lust within their heart and soul are very real, and the feelings of hurt and betrayal in your heart are also real. Plus, regardless of their proclaimed initial intention of not taking it any further, this is a VERY slippery slope as far the risk of gradually changing your view of the relationship as the fog of a sexual or emotional relationship develops. There is a very real danger of a fantasy computer relationship leading to greater and greater feelings of attraction which can eventually lead them to push aside and discount their real love for you. They may fool themselves into thinking this isn't for real, but at any moment their head is just a mouse-click away from agreeing to a real-life rendezvous, which they might justisfy as innocuous and intended just to satisfy their curiousity. However, given the emotionally or sexually charged atmosphere of their internet communications, there is a very great danger and temptation of this leading to an actual sexual liason, or at least a long term emotional or sexual infatuation.
You should treat this exactly like a real emotional affair, or as a series of attempted affairs. You need to tell your spouse that your feelings ARE REAL, that you are hurt and betrayed by his sharing sexual excitement with other women. When you have some composure, you need to calmly ask him to imagine that he is in the other room, sick or otherwise limited by a health problem, and have him imagine that you are chatting online and exchanging sexual flirtation repeatedly with other men, exhanging emails with men from singles dating websites, repeatedly communicating with the same men, and sharing feelings of lust, sex, and fantasy with them. Then ask him, would he feel betrayed or cheated on if you did this behind his back?
Many people have these problems with their spouses because of the internet's anonymity, ease of access to so many people out there, and it's seemingly safe and secretive environment. His sharing sexual thoughts or deep emotions with women by any method IS cheating on an emotional level, and doing this behind your back is cheating, and if he continues he is betraying you and is aware that he is betraying you.
I agree with the other person, get a keylogger and install it. Do a few internet searches as some are cheaper/better than others. Also, read his cellphone records and look for unexplained calls/numbers. Cyber sex usually/often leads to phone calls, and that sometimes leads to a physical rendezvous. His excuse is BS - he is being tempted by forbidden fruit, and if he practices chasing women via internet communications, you can bet this hungry, drooling hunter eventually will be so intoxicated by the sexually charged emotions that he will not say "no" when he finally catches his prey.
You should insist that he cut off all contact by email, internet messenger, or cellphone, and that he share his email password so you can verify he has done so. Tell him if he does not do this you will feel like you can't let go of the hurt or betrayal, and you will feel like he doesn't care if he risks losing you. Tell him there is not room in your life for him and his chasing of other women on the computer. These are real people and real feelings he is dealing with. If he has nothing to hide, then there should be no reason why you cannot read his email. Tell him he has to do this in order for you to heal from this misbehavior, or else as time goes on, this will eat you up inside, make you distrust him further, resent him, and feel he is locking you out of his private life to be able to cheat even more. Married couples should have nothing to hide from one another.