What is the name given to a woman who never marries?

"During the Elizabethan era, spinster came to indicate a woman or girl of marriageable age who was unwilling or unable to marry. Nowadays, it usually connotes an "old maid", a woman who, for any reason, remains unmarried.

Both of These terms have fallen out of usage, so a woman who never marries is modernly called a "bachelorette"; this term is more recent, having been popularized by the matchmaking show of the same name (Wikipedia "Bachelorette").

The French term for women single over 25 is "Catherinette"; they have a feast to celebrate this event, "while everyone wished them a fast end to their singlehood."