Not, as popularly assumed, named for any romantic qualities, the Romance languages are languages descended from the language of the Romans; namely, Latin.
The most familiar Romance languages are those that are national languages of Western Europe: Spanish, Portuguese, Italian, French.
However there are and have been quite a few 'minority' Romance languages, whether parallel descendants of the original Vulgar Latin or "merely" dialects or offshoots of the major languages. The following is a list of Romance Languages from SIL's Ethnologue.
Per request, major languages are in bold.
English is not a Romance language. It is not descended from Latin, although it has a huge amount of borrowing from Old French, due to historical circumstances (Norman invasions, IIRC). English and Latin are related however; they are both Indo-European languages, whose reconstructed ancestor proto-Indo-European gave birth to a wide range of other languages such as Greek, Sanskrit, and Yiddish.