Online chatting while in a serious relationship?

If you have been in a serious relationship for five or more years with someone and you constantly find out they have been chatting with other women online, would you be angry? Would you break it off with them after constantly asking them to stop? If they used Yahoo Messenger and kept adding "friends" who are women and typical messages say things like "I want to wrap your legs around my neck" or "you look so good and sexy" or "I'd love to see you naked", etc...would you be furious with them?
I think it is wrong to flirt that heavily with anyone else, no matter what. I think it's emotionally draining them so that when you come along, they don't pay as much attention to you. Even with an incredible sexual relationship with this person, you wonder why they feel the need to constantly look and flirt with others online.

I hope to hear from both men and women on this subject because it seems like the answers will be different. Men might say that if they aren't physically doing anything, there's nothing wrong with it. Many women might say it's emotional cheating and can lead to physical cheating if they were to meet. The lies about it are hurtful enough, but seeing what was actually said to these online skanks is very heartbreaking. If you are in love with someone and you tell them what hurts you, wouldn't they stop doing that if they knew it bothered you? What do you think and what would you do?