Setting aside my own personal favorites, I would introduce you by order of legend and popular stature, and then if your interest is at all piqued, work your way into the good stuff.
Start with Annie Hall and Manhattan, followed by Bullets Over Broadway and Hannah and her Sisters.
If you go for those, do Purple Rose of Cairo and Crimes and Misdemeanors.
After that, Husbands and Wives (my personal favorite), Stardust Memories, Zelig, and Radio Days.
Once you've made it that far, it's a free-for-all; just dig in, and you won't be disappointed (except maybe for the last 3 Allen films and some of the pre-Annie Hall stuff, though Sleeper is much better than you might think, even in comparison to his later, more cinematic work).
Good luck, and enjoy.