Ehh, couple things that have been touched of but still want to reply to.
The whole actors-knowing-your-name thing I would not at all use as stalkerish critera. I mean, there's difference reasons for everyone. Some actors are very personable and after a conversation, long or even at a stage door, will make the effort to remember your name, or even if something catches them. I've also had a friend who is friends with a couple of broadway stars, and they know me through her...it is kind of cool that they know my name too, but I agree with CJR, it's okay as long as it's not from a restraining order.
I've actually done some of the going to the stage door of a performance I haven't attended for a number of reasons. I used to attend lots of matinees, and some wouldn't come out after the matinees, so like Spamalot I got a couple of supporting cast members after a matinee and another night I saw Altar Boyz, which ended way before Spamalot, so I decided to head over Spamalot to try to get a bit more autographs/pics, that's often why I'd do this. Rarely I may want to talk to an actor from a show I'm not interested in seeing and so I'll go to that stage door. However, often I just do it because I'm seeing another much shorter show and figure might as well while I'm already in the city and a show will be letting out early.
One last thing...someone asked how you know when it's right to approach a person...well, I would usually exclude eating from this, as if I saw a broadway actor eating I would not interrupt their eating, but perhaps if I wanted to just say you were great in blah, blah, I'll watch for when they get up to tell them-when I used to take road trips to see the Yankees, I'd see some of them at restaurants, and would only ask for autographs once they got up. In other terms, walking down the street, even alone or with others, I think if you give well an easy out it's okay...like just to say a quick I saw you in this show, I thought you were great...then that kind of leaves it up to the actor from there. If they're tired or are otherwise occupied, they can say a quick thank you and continue on, I'm sure most actors wouldn't mind a quick compliment. And other times, you might find that the actor is just incredibly nice and have a 15 minute conversation with them...
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli