.
X-Men:
Claremont's Uncanny X-Men (at least through the Dark Phoenix Saga): Pretty much redefined X-Men before Morrison came along and did it again. Be wary that the dialogue is very dated, however.
Morrison's New X-Men: Though I don't like the last few arcs, specifically Planet X, it's still highly recommended reading. Especially for an X-Men fan. Though the art is all over the place.
Whedon's Astonishing X-Men: Basically a loose sequel to Morrison's run (not necessary, but it gives Whedon's run more impact), it brings the X-Men back to being superheroes. Whereas Morrison focused more on the politics of it all. Whedon's run has been my favorite run so far. It has a lot of heart, and has a very emotional ending that made me tear up a lot. Not very many books can claim that.
Bendis' Uncanny X-Men: Not necessarily required or definitive at all. It didn't do anything particularly special, but I enjoyed it a lot. It has some genuinely cool moments. Though, if you don't like Bendis, I wouldn't read it. Plus, reading All-New X-Men for the first few arcs is pretty much required, since a good chunk of UXM's story begins there. I'm not exactly a fan of ANXM, though. Final issue of UXM is pure aces, though.
Other books:
Remender's Uncanny X-Force: Next to Whedon's AXM, this is my favorite X book. Redefining Apocalypse (which is still used now) and writing my favorite version of Deadpool. It has some really strong arcs, both plot and character. It's a very dark book, however, generally dealing with the theme of whether or not killing is always the best way to solve a problem (assuming it's an option). Plus it leads up to Remender's Uncanny Avengers, which is also awesome.
Rucka's Cyclops: This book does have more than just Rucka as a writer, but Rucka's initial run is the best. Just a fun space pirate adventure with young Cyclops and the Starjammers. Also a great Cyclops story, even if it is the O5 Cyclops.
Spurrier's X-Force: Again, a very dark and violent book dealing with "how far is too far), but still really good. If you like the good guys being not-so-good guys, this book is perfect. It also has one of the best retcons in a long time (Forget-Me-Not).
X-Men: Age of X: Just a really cool alternate timeline story. Not much beyond that. It gets referenced in Spurrier's X-Force.
Hope that helps, It's just off of the books that I really liked. There are a couple others, but I haven't read a whole lot of them to really recommend them. Those are all books that I've read the whole run of (save for Claremont, but through the Dark Phoenix Saga is a lot).