Everything everyone SHOULD watch.
(In no order)
Tengen Toppa Gurren Lagann
Great Teacher Onizuka
Death Note
Durarara
Cowboy Bebop
Samurai Champloo
Full Metal Alchemist
To Aru Majutsu no Index/Kagaku no Railgun
You will probably have seen some, if not all of these. But they are definitely worth watching if you haven't already.
If you want to watch more recent anime, try these ones.
AnoHana
Angel Beats
Bakemonogatari
Most of the new ones really depend on your tastes so i won't suggest too many.