I am on the shady side of middle age and I still like to occasionally go to the stage door. I've introduced out of town friends to the practice and, years later, they still talk about 'meeting' Harvey Fierstein or John Lloyd Young and then watching them subsequently win the Tony.
Oftentimes, I'll just hang back and observe the crowd. It's like Act III sometimes. I love the energy that the young people exhibit when they see a favorite show of theirs. Generally I won't bother with an autograph, unless it's a big star like Angela Lansbury or Chita Rivera. If an actor is leaving the show, I do make a point of congratulating them on their final performance (John Tartaglia, Jason Tam), or telling an understudy how much I enjoyed their performance (Yuka Takara, Taylor Frey, Rich Ceraulo). I've been fortunate to meet great people of the theater, such as Joseph Stein and Jerry Herman, just by hanging out quietly at the stage door. And Alvin Ing invited me for drinks one night after FLOWER DRUM SONG in Sacramento (he doesn't drink and I was driving, so we just had coffee, but what a thrill that was).
And, yes, sometimes I will go to the stage door just to get the autograph of an actor who I just find so irresistibly handsome, I simply must meet them in person (I'm talking about you BD Wong, Cheyenne Jackson, and Telly Leung)
'Our whole family shouts. It comes from us livin' so close to the railroad tracks'