Learn English – What do you call someone who hates people with mental disabilities

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).

Perhaps self-absorbed

absorbed in one's own thoughts, activities, or interests

or egocentric

regarding everything only in relation to oneself; self-centered; selfish

or self-centered

concerned solely with one's own desires, needs, or interests

SUPPLEMENT

Also consider self-directed

(of persons) free from external control and constraint in e.g. action and judgment

Note that this term is often applied to someone who does attend to the needs of other but exerts a good deal of independence in doing so.

and autonomous

Not controlled by others or by outside forces; independent