They gave me one of those things, like a nomination, two or three times, Johnny says. A nomination is plenty.. Johnny Depp's had three Oscar nominations up to this point for his roles in Finding Neverland (2004), Sweeney Todd (2007) and the first Pirates of the Caribbean film (2003).Image caption Johnny Depp was with wife Amber Heard for the British premiere of Black Mass. Captain Jack Sparrow is never far away.hey gave me one of those things, like a nomination, two or three times, Johnny says. A nomination is plenty.. Johnny Depp's had three Oscar nominations up to this point for his roles in Finding Neverland (2004), Sweeney Todd (2007) and the first Pirates of the Caribbean film (2003).