Romance describes a story that deals with love between two or more characters typically also having an optimistic ending.
Romance — Subcategories
A love polygon refers to a romantic relationship involving n people. Although a love triangle is not limited to just heterosexual relationships, in anime, it usually deals with two females liking one male and vice versa.
Shoujo Ai means girls love, and as such it explores what happens when two girls fall in love. This is not to be mistaken for Yuri which is a hentai genre. This is not. Meaning no graphical sex.
Shounen Ai means boys love, and thus explores what happens when two boys fall in love. This is not to be mistaken for Yaoi which is a hentai genre. This is not. Meaning no graphical sex.
Sudden Girlfriend Appearance
Sudden Girlfriend Appearance anime involve a sudden change in the main character's life where (s)he suddenly gets confronted with an individual (s)he's sexually attracted to, the two of them inevitable becoming a couple.