1. The Godfather trilogy
2. Goodfellas
3. A Bronx Tale
4. Scarface (the 1932 original starring Paul Muni)
5. On the Waterfront (Marlon Brando)
6. The Roaring Twenties (James Cagney)
7. Little Caesar (Edward G. Robinson)
8. Angels with Dirty Faces (James Cagney, Pat O'Brien)
9. Casino
10. The Brotherhood (Kirk Douglas)
11. Mean Streets (Harvey Keitel, Robert DeNiro)
12. White Heat (James Cagney)
13. Valachi Papers
14. The St. Valentines Day Massacre (Jason Robards)
15. Honor Thy Father

If you have another choice you feel ranks alongside these classics, by all means please list it.

PS: I add a few suggested at the bottom I thought should rank as well.