Girlfriend/Boyfriend: These are gendered terms that do not convey a measure of commitment to the relationship. These terms are fine at the beginning of a relationship, but could be problematic after cohabitating for over a year, especially to achieve common-law status recognition.
Wife/Husband: These are gendered terms that are often perceived to convey heterosexuality. They also convey that the relationship has been sanctioned through a ceremony officiated by a religious or government body.
Spouse: This term is not gendered, and often used instead of wife/husband. However, it is an emotionless term that seems more appropriate when used in formal circumstances, or on application forms.
Common-Law Spouse: This is also an emotionless term. It conveys that one is in a long term committed relationship akin to a marriage but without the official sanction of religious or government body.
Significant Other: This is too formal a term to signify a person with whom one shares a long-term intimate relationship.
Partner*: Another emotionless, unromantic term. It is also ambiguous since it can be misconstrued to reflect a business, legal or an entrepreneurial relationship. You would need to clarify the partnership, for example: Life Partner, Sexual Partner, Live-In Partner, Domestic Partner.
Companion/Cohabitant*: These are ambiguous and emotionless terms that do not necessarily convey the status of an intimate, loving and committed relationship.
POSSLQ: According to dictionary.com, “…(/ˈpɒsəlkjuː/ POSS-əl-KYOO, plural POSSLQs) is an abbreviation (or acronym) for "person of opposite sex sharing living quarters", a term coined in the late 1970s by the United States Census Bureau as part of an effort to more accurately gauge the prevalence of cohabitation in American households.” However, this term is only applicable to heterosexual relationships, and has no bearing on intimacy or commitment.
* Note on Live-In Partner, Domestic Partner, and Cohabitant: These terms are also problematic in that many people today are choosing to be in intimate, long-lasting and committed relationship without necessarily living together. Examples include Long Distance relationships, or people who choose not to share their living arrangements or other familial or financial obligations. The reverse is also true: many people share living quarters but are not in intimate relationships.