What do you call someone who betrays his/her spouse sexually?
Solution 1:
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).
Solution 2:
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.
Solution 3:
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.
Solution 4:
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.