What is a word for a person you live with but are not married to? I do not mean a room mate, but rather someone you are romantically involved with. From what I understand, spouse is someone you are married to and boyfriend/girlfriend does not state that you live together.
"Common-law [husband|wife|spouse]" implies a understanding that a state of marriage exists but that you have not bothered getting official sanction.
Unmarried people living together are sometimes said to be "cohabitating", which suggests "cohabitant", though I've only heard that phase used once and it admits a misunderstanding that it merely means sharing a dwelling.
A possible term for this is significant other. This is defined as:
A person, such as a spouse or lover, with whom one shares a long-term sexual relationship.
This is a word I often hear used to described a long-term partner with whom a person lives.
The phrase live-in girlfriend or boyfriend is sometimes used. Domestic partner also describes the situation, but in recent years it has come to refer to homosexual partnerships more often than heterosexual ones.
The (United States) Census Bureau originated a phrase which became quite popular circa 1990 or so: POSSLQ, pronounced "possle-cue". It stands for Persons of Opposite Sex Sharing Living Quarters.
Such a bureaucratic, unromantic phrase... and yet I recall that my POSSLQ and I got a kick out of calling each other that. Good times.
Basically, if you act like a married couple, and you're just missing the official piece of paper, you can get away with using words like husband, wife, and others that are typically reserved for legal marriage.
To inject a personal anecdote, after my father died, my mother began seeing, and eventually living with, another man. They had intended to get married, but things got in the way (planning my sister's marriage, then illnesses) and they eventually decided it wasn't really necessary. But after a while, she started referring to him as her second husband, and everyone accepted it. She'd become close to his family, considered his children (all grown) to be hers. When his grandson had a child, she announced that she was a great-grandmother.
Here in Australia at least, this would be referred to as a de facto partner, de facto being a Latin expression meaning 'by fact'. That is, a partnership for all intents and purposes but not a marriage by law. This term is used commonly in government regulations concerning taxation and social security as it implies cohabitation, sharing of financial responsibilities and so on.
Having said that, de facto would rarely be used by someone to describe their partner, it being more of a legal term.
One possible word is paramour.