Suggestions: beloved, sweetheart (Arabic: habibi) mi amore (Italian), my love, my darling, companion de vie (French, though not sure I spelled it correctly), honey. "Companion" seems common among retired people, but that can also be a weird euphemism or casts doubt on whether they even are or can be romantic, or whether they just like to travel together. "Fellow traveler" for science fiction fans. For long, "the other half of my heart." "Better half" is a humorous term and I have heard it used mostly by men to refer, in a complimentary way, either to their own wives or to their friends wives (also mild insult to the friend, but not necessarily).
"Significant Other" is actually a social science term, and it INCLUDES one's children, parents, really important friends or anyone who is personally quite important to one. I am a social scientist and I find this too broad, and also terribly unromantic. Though it is in common use. "Adult attachment figure" would be a psychological equivalent. Ick, right? Likewise, POSSLQ (poss-uh-queue): which I think stands for person of opposite sex sharing living quarters -- a term from the census. Distinctively impersonal unless tongue-in-cheek.
"Partner" is the term lots of people are using, to not exclude those in committed relationships who may or may not be married (was especially inclusive when or where gay & lesbian marriage was illegal. Its also gender-neutral and egalitarian. Personally I also don't like this because my connotation with partner is business partner or legal partner, and that again doesn't convey the lovingness and personal and emotional bonds of the relationships we are discussing. "Life partner" at least is better.
A few commentators do not seem to be distinguishing between how you would address one's beloved, and how one would refer to one's beloved to other people. Private and public terms can be different if you both want a private term or terms.