This started as a comment to Silenus's answer, but it got too long.
It would depend a lot on context.
If the other person is complicit in the act of cheating then Mistress is often used. Also used are other less direct, derogatory terms.
John's mistress was well aware that he was a married man.
If the other person actively seeks a relation ship with the married person, Home wrecker is used. It's important to note that in the case of Home wrecker, it's implied that the person doing the cheating is less responsible, then the person cheating in the mistress situation. How much less depends on culture and audience.
That young home wrecker Janet, enticed my husband into cheating.
Lastly, if the person with the cheater is not aware that the cheater is cheating, normal terms are often used to avoid placing blame on that person.
I feel sorry for Jake, he had no idea Susan was married.
Also point of view matters.
For example "Jake's paramour, Jill.." tends to imply that Jake was in love with Jill, though married to someone else. It would come of really odd to say that a group or more then one person had paramours. For example "All the cheating women had different paramours" really is quite odd. "Paramour" tends to imply love (originally meaning "For love").
Lover on the other hand tends to imply only a specific physical relation ship. "James's lover, Beth, met his wife today."
By contrast, you may be more sympathetic to Jake, after all he just wants to be with the woman he loves, but James needs to learn how to handle himself better.