Also, 16 is an excellent age to get into these films. I watched them my senior year in HS when I was 17. Instantly fell in love with them. And it's a love affair going on ten years. God... has it been that long already? I remember watching these films for the first time like it was yesterday.
Anyway, about watching these films as a teenager: They are still "cool" enough to hold teenagers attention, but the films contain enough "quality" to really propel teenagers into more complex art, both in film and literature.
If I had never seen the Godfather, I really don't think I would have ever been drawn into the classics... Citizen Kane, Casablanca, Gone with the Wind...
It opened my eyes to an era of cinema (th one before the year I was born, LOL) which up until then, I had pretty much ignored.