I give the super-hero, you give me the first (and/or second) definitive Story-arc
Legion of Super-Heroes:
Great Darkness Saga, obviously.
Hal Jordan:
I'm gonna say Hard Travelling Heroes because Neal Adams signed my copy of the TPB.
Avengers:
Didn't read any Marvel growing up, so I couldn't say.
X-Men:
Age of Apocalypse really summed up the 90s in a lot of ways, with "Alpha" and "Omega" issues, foil covers, temporary renumbering, and a fake death undone months later.
Flash:
The Return of Barry Allen. Turned Wally West into a main eventer for good. Too bad they now hate him for some reason.
Spider-Man:
For better or worse, the Clone Saga.
JLA:
Tower of Babel.
Hulk:
Never read Hulk until very recently. I really liked the last run of the title, though, with Hulk and Banner trying to outsmart each other with a series of seemingly impossible deathtraps.
Captain America:
I've been reading the Steve Englehart stuff from the 70s with the Falcon via the Essential collections and really enjoying it, but I don't know that much of it is "definitive" because I was never a Marvel guy.
Batman:
Bare chested Batman fighting Ra's Al Ghul in the desert with awesome Neal Adams artwork. You can also say Tower of Babel here.
Teen Titans:
The Judas Contract. I still re-read that TPB all the time.
Thor:
No idea, never read anything from the character, although I really loved the movie.
Fill in any you like.