Great thread. I mostly watch those which are the consensus best of the bunch. I don't consider myself an otaku, or an expert in the subject, but I know several people who are very knowledgeable about anime/manga. I have also watched plenty of old and new, so I can give an opinion too. Here's a list of the anime/manga I've enjoyed, and are my recommendations to anyone looking for a good to great experience.
In no order, those I remember right now:
(Genre list taken from www.animefreak.tv
, for those that haven't watched some of them)
Berserk : Action, Adventure, Demons, Drama, Fantasy, Horror, Romance, Supernatural, Military, Seinen
Darker than Black: Action, Mystery, Drama, Sci-Fi
Black Lagoon: action, seinen
Rahxephon: Action, Mystery, Drama, Mecha, Romance, Sci-Fi
Death Note: Mystery, Drama, Supernatural, Police, Psychological, Thriller
Claymore:Action, Adventure, Drama, Fantasy, Shounen, Supernatural
Code Geass:Action, Drama, Mecha, School, Supernatural, Military
Cowboy Bebop: Action, Adventure, Comedy, Drama, Sci-Fi, Space
Xam'd Lost Memories: Action, Sci-Fi
Tengen Toppa Gurren Laggen:Action, Comedy, Mecha, Sci-Fi
Soul Eater: Action, Adventure, Comedy, Fantasy, Shounen, Supernatural
Samurai Champloo: Adventure, Comedy, Samurai, Shounen
Baccano: Action, Adventure, Fantasy, Historical, Seinen
Those come to mind right now. I'm sure there are a few others I'm forgetting. I've watched Naruto, Bleach, etc. too. Without filler episodes these are good too.
I've watched many oldies too, some very unknown. My childhood favorites were Saint Seiya, DBZ, Rurouni Kenshin, etc.