For the majority of people, adultery is morally wrong. There are cultures or situations in which taking on a second -- or third or fourth -- romantic partner may be considered acceptable. But, in general, finding out or deciding to be the other woman may stir up ethical issues. You'll have to deal with your own feelings on this subject. If the man admits he is cheating, has no plans to leave his spouse and wants to keep you as his "secret," consider your moral viewpoint on the issue of adultery. If it's in no way acceptable to you, it's time to leave the relationship.
As the other woman, you aren't obligated to provide a promise of commitment or monogamy. Unless your guy is leaving his spouse for you, keep in mind that she is his wife and he is the cheater. Remaining committed or faithful to a married man who has no plans to eventually be with just you closes off your more realistic options for a relationship. Handling your "other" status may mean that you enjoy the time you spend with him, while keeping an eye out for other romantic possibilities on the horizon.
Once a Cheater
If your guy insists he's ready to leave his wife and take you from "other woman" to the "only woman," take some time to consider if he can change his ways. While it's possible that he didn't know what love truly is until he met you or he married the wrong person, it's also possible that he's a serial cheater. In a study on attitudes on infidelity as predictors of fidelity in the journal "Current Psychology," people who held either morally ambiguous or deceptive types of attitudes were more likely to engage in those types of behaviors than people who didn't. If your guy already has a deceptive attitude, consider the possibility that he'll find another "other woman" later on.
Avoid seeing yourself as a victim. While it's possible that you got into the relationship thinking that he was single, you have the power to either stay or go. If he lied to you about his wife, you're seeing his dishonest side right from the start. Instead of dwelling on the fact that he hurt you, take a stance and walk away. If he was upfront from the start -- and you still went ahead with the relationship -- remember that it was your choice.