The cheater can be the guy or the girl and it can be revenge drama or the couple working on their marriage after the affair. I just want romance. Thank You!

Off the top of my head, I would suggest:

I Need Romance.  They aren't married, but they've lived together for 10 years, and the man cheats pretty early on. 

Birth of Beauty.  This is definitely a revenge plot - some of it is geared towards a man cheating, but there are some other factors also.

A Gentleman's Dignity.  One of the main characters is a serial cheater.  Definitely more on the comedy side.

Discovery of Romance.  Two people in a serious dating relationship.  They both find other people they really want to be with, but they still carrying on their relationship.

Full House.  This isn't about cheating exactly, but both parties (mostly Rain) are more interested in other people for most of the drama.   It almost brings about the same feels of a cheater plotline (at least it did for me).

Good luck in your search!  I'm sure there are lots of other options for you that I couldn't think of.
Secret Love Affair - Woman in loveless marriage falls for younger man. It's a drama about forbidden passion, dreams and music, but also about complicated family, friendship and business relationships. http://mydramalist.com/8929-secret-love-affair It's a good one. 

Valid Love - Happily married couple, the woman falls madly in love with another man. The focus of the story is how torn she is between the two men, the heartache of all the characters, the husband's pain and love for his wife and how they all try to figure out what to do. There are also supporting characters who are not too much in the way of the main plot. I liked this drama. I found it hilarious at times, sometimes painfully emotionally intense. Personally I found parts of it a bit annoying and draggy towards the end, but I like the way things were resolved. http://mydramalist.com/10874-valid-love

Hirugao - The two female main characters live in loveless marriages. One is a rich "trophy wife" who cheats on her husband to get some excitement in her boring live, knowing that her husband doesn't love her anyway. The other is a part-time working housewife who is hurt by the fact that her husband is not interested in her as a woman anymore. The two women become friends and things start to happen. The rich wife starts and affair with a brooding artist, and the other one falls for a biology teacher who finds that his relationship with his wife isn't going so well. I LOVED the first half or so. The opinions of the ending differ; I don't know what you like, but you might enjoy this drama. http://mydramalist.com/10447-hirugao

Sayonara Watashi - The focus of this drama is the friendship between the two female main characters, who swap bodies in the first episode... One of the characters is married, and he finds out that her husband is having an affair with the friend. I found this to be a pretty interesting and unusual love triangle, especially with the way it ended. :) http://mydramalist.com/11368-sayonara-watashi

Mitsu no Aji - The main characher falls in love with her father's younger half brother, a doctor who gets married to a co-worker. A lot of people hate this drama but personally I enjoyed it a lot despite the incest theme. http://mydramalist.com/3006-mitsu-no-ajia-taste-of... (Kanno Miho is great in this drama by the way.)

Koi - The main character falls in love with a literature professor and his wife, who has many lovers and her husband is aware of it. It's a "special" so it's more like a movie than a drama, but still. Loved it. http://mydramalist.com/8320-koi