Well, I'm from NYC, so whatever I say about this will come off as either boasting or cheating, but I've seen lots and lots of live theater. Most of the Broadways stuff I've seen I got the tickets comped and I really hated the productions.
On Broadway, I saw:
Evita, with Patti Lupone (bad show, but she was great)
Pirates of Penzance, with Kevin Kline (brilliant production), also saw this in Central Park
Cats, orig cast (sucked)
Annie (sucked)
Master Harold and the Boys (best Broadway show I've seen)
Phantom of the Opera , with orig cast (really really terrible, left at halftime)
among others
For several years I saw OB and OOB productions about once a month, mostly avant-garde and absurdist things and 'new' theater like:
Ionesco: The Chairs, The Bald Soprano
Euripedes's Medea, staged by Joanne Akalaitis (!!!)
Ibsen: Miss Julie, The Dollhouse
early Sam Shepard, like Fool for Love (OOB, with Sam in the lead)
Aeschylus's Agamemnon
everything by The Ridiculous Theatre Company with the late, great Charles Ludlam
Genet's The Maids
I've also seen Richard II, A Midsummernight's Dream, and The Tempest, all in Central Park's theater.
I also went through a period of seeking out English Restoration comedies, like The Country Wife.
Lots of original productions on short runs, and of course when I was a kid I went to all the obligatories—Sound of Music, Shenandoah, Oklahoma . . . my school had an annual thing up in the nosebleed area.
The best single staged piece I've ever seen was Bertolt Brecht's Mother Courage in a small production in which the players were 'shadowed' by other actors performing in American Sign Language.
I really can't remember everything I've seen.
Oh, once I saw Faye Dunaway in a really tiny theater production in Hampstead, London. Something about a presidential assassination.
BTW, SFG, I think it's really funny that you used the word 'attend' instead of 'go to'. Makes it sound like some kind of obligation or punishment.
Edit: Must include my son's latest appearances in The Music Man, Annie Get Your Gun, and Guys and Dolls.