For a word that can refer to both married people or people in a relationship, you can use cheat , cheater , two-time (informal).
Two-time is also used as verb, as reported from the NOAD:
He was two-timing a fiancé back in England .
For people who are married, you can use adulterer (which is gender-neutral) or adulteress (when referring to her).
english.stackexchange.com/users/252/kiamlaluno
Adulterer is gender neutral but refers specifically to a marriage, not other relationships.
edit:
Merriam-Webster lists a female form, adulteress , but it seems to have fallen into disuse.
english.stackexchange.com/users/4973/Yitzchak
The term philanderer could be used, although it is more rare and often used along with the other terms mentioned (adulterer/adulteress/two-timer/cheater).
The person who engages in philandering is a person who engages in at least one, if not many frivolous sexual exploits outside of the bounds of marriage.
Philanderer has a strong male connotation.
I have not heard this term used in reference to females.
You dirty, rotten, two-timing, cheating, adulterous philanderer!
I trusted you!
When referring to an unfaithful woman, sometimes much more vulgar terms are used, usually in relation to her sexual morals and/or her potential willingness to engage in prostitution.
english.stackexchange.com/users/3328/Zoot
Most commonly the betrayer is referred to as an adulterer, although cheater works as a more colloquial term.
I'm pretty sure it is gender neutral, as well.
english.stackexchange.com/users/4944/Nick Coelius
The technical/formal/old(?) term is adulterer/adulteress.
The term used by ordinary people in not-extremely-formal contexts is cheater.
english.stackexchange.com/users/2701/Jürgen A. Erhard
Cheating on one's spouse is not the only way to betray them; there are several others e.g. disclosing a spouse's deepest secrets, causing your spouse some form of public humiliation, etc.
If the betrayal involves sexual escapades or an illicit/extramarital affair, then relevant terms are: cheat
• womanizer • skirt-chaser • adulterer[ress] •
fornicator • heartbreaker •
philanderer • husband-snatcher • two-timer • unfaithful spouse • ladies' man • seductress
•
Don Juan • Casanova
english.stackexchange.com/users/2705/Jimi Oke
The word for a man/woman who is married and has sex with a woman/man who is not his/her wife/husband is adulterer/adulteress
english.stackexchange.com/users/None/
While English does retain some nouns for a person who displays infidelity in a marital relationship, these terms have the sense of being curiously dated.
To call a person "a cheat" or "a philanderer" harkens back to the kind of language you'd hear in some Doris Day-Rock Hudson comedy from yesteryear.
It is possible to say, "he's an adulterer," but to do so is branding the person with an identity, and socially it's becoming less permissible to do that.
Rather, the more common ways to express this sort of thing is through more active terms that describe the activity itself:
He's cheating on her.
She's seeing another man.
He was unfaithful to her.
She went around behind his back.
Etc.
english.stackexchange.com/users/5262/The Raven
From a British perspective, I would say that cheat (exactly the same spelling as the verb) and two-timer (with an r ) are the standard nouns describing people outside a marriage.
Cheater is used colloquially, but is frowned upon as incorrect.
Two-time is used as a verb, not a noun.
As others have stated, adulterer and adulteress are the standard, formal terms for people within a marriage.
english.stackexchange.com/users/5654/Rick
Perhaps not PC, but in English common law betrayal of one's husband (or lord) was called petit treason.
However this tended to be for extreme betrayals: a knife in the back where the blade was rather more solid than a metaphor.
english.stackexchange.com/users/7662/Fraser Orr
A philanderer can be a person who is not married.
english.stackexchange.com/users/77211/guest
Works for both man and woman: Bedswerver
One who swerves from and is unfaithful to the marriage vow.
english.stackexchange.com/users/69857/Third News
It is infidelity or an affair (marriage) vs cheating "the game" and its "players" and "sluts" on both sides, when it comes to dating.
Most marriages are just a pipe dream between two "players" who regain their love for "the game" eventually.
Well, on average it takes seven years; Then the carriage turns back into a pumpkin.
english.stackexchange.com/users/83091/user8230
What do you call someone who betrays his/her spouse sexually? Is the word different for men and women? Is it different for people who are in a relationship and not still married?
What do you call someone who betrays his/her spouse sexually?
english.stackexchange.com
<word-choice><single-word-requests><pejorative-language>
english.stackexchange.com/questions/12490
english.stackexchange.com/users/3782/Manoochehr
For a word that refers to both married people or people in a relationship who betray their partner, you can use "cheat", "cheater" or "two-time". For people who are married, the term "adulterer" can also be used when referring to a man and "adulteress" when referring to a woman. Sometimes more vulgar terms are used when referring to an unfaithful woman. The word "cheater" can be used for both male and females who are not loyal to their partner. "Two-timing" is another term used in the UK.  For married partners "adulterer" is the term used, although some consider this an older term. "Philanderer" is also used solely for a man, who has sexual affairs outside marriage. There are more derogatory terms used for women equating her to a prostitute. Some feel "cheat" and "philanderer" are old terms whereas "adulterer" is more modern. Some consider "cheater" as a colloquial expression.  A philanderer can also be a person who is not married. Another older term from French is "petit treason" and again another term suggested is "bedswearver" for both male and females.
For a word that refers to both married people or people in a relationship who betray their partner, you can use "cheat", "cheater" or "two-time". For people who are married, the term "adulterer" can also be used when referring to a man and "adulteress" when referring to a woman. Sometimes more vulgar terms are used when referring to an unfaithful woman. For married couples, adulterer can be used, but it is more formal and antiquated than other terms. Cheater is the most common term that applies to any relationship, although terms like two-timer and philanderer can be used in some contexts. More colloquial terms include womaniser, skirt-chaser, husband-snatcher or bedswerver.
The word for a man/woman who is married and has sex with a woman/man who is not his/her wife/husband is adulterer(gender neutral)/adulteress(female). Other terms that can be used for both married people or in relationships  include betrayer, cheat or philanderer. More informal terms include; cheat or two-timer. The gender-neutral term for someone who sexually betrays their spouse is "adulterer" or "adultress", although "cheater" is also used in colloquial speech. Other terms that may apply include "bedswerver" or "philanderer".
If the betrayal involves sexual escapades or an illicit/extramarital affair, then relevant terms are: cheat He was two-timing a fiancé back in England .
If the betrayal involves sexual escapades or an illicit/extramarital affair, then relevant terms are: cheat He was two-timing a fiancé back in England .
There are numerous terms that can be used. Some refer to men only, and some are colloquial. Philanderer Women cheating. The modernity of the terms
For married couples, adulterer can be used, but it is more formal and antiquated than other terms. Cheater is the most common term that applies to any relationship, although terms like two-timer and philanderer can be used in some contexts. More colloquial terms include womaniser, skirt-chaser, husband-snatcher or bedswerver.
The technical, gender-neutral term for someone who sexually betrays their spouse is an adulterer or adultress. "Cheater" is generally an accepted term for this in colloquial speech. Some terms that might apply in this case are "bedswerver" or "philanderer".