Everything everyone SHOULD watch.
(In no order)
Tengen Toppa Gurren Lagann
Great Teacher Onizuka
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.
Most of the new ones really depend on your tastes so i won't suggest too many.