'Ain't' is slang or non-standard dialect and has no place in proper English.
All major English dictionaries list 'ain't' as a real word, though most mark it as non-standard, dialectal, or informal. The term emerged in 18th-century English as a contraction of 'am not,' 'is not,' or 'are not' and has been documented in literature for over two centuries. Its pedigree is impeccable: it appears in works by Mark Twain, Louisa May Alcott, and other canonical authors. The stigma against 'ain't' is a classic case of class-based linguistic discrimination, it became associated with working-class and African American speech patterns, and prescriptivists accordingly dismissed it as 'incorrect.' Linguistically, it's entirely systematic: it fills a gap in English (we lack a unified 'is not' contraction), making it functionally useful.