Derived from Brum, from Brummagem, being Birmingham.
Also an adjective as in brummie accent, brummie sense of humour and 'brummie goit'. Compare to scouse, Cockney and yellowbelly.
For your actual stereotypical brummie, see Timothy Spall's perfomance as the computer game technician in Red Dwarf, series five, Back to Reality. For standard abuse of brummies, see Rimmer's response: "You brummie goit!"
The brummie's brummie is to be found in Dudley or, as we prefer to call it, "Doodloy". This is despite the fact that Dudley is in the Black Country (and its inhabitants are therefore yam yams); most non-brummies do not see the difference.