i'd have to say Neon Genesis Evangelion, just because it was the first anime series i properly watched, and mindfuck as it was at times, i totally respected what it was trying to do.
I think Cowboy Bepop is a super close second though. While the main storyline could've perhaps run through more of the episodes instead of a few (which i felt Samurai Champloo improved upon), the character development was pretty great. Also... best original soundtrack ever... for anything. It just seemed greater than the sum of its parts, and had an impact on me which i totally didn't expect.
When i think about it, Welcome to the N.H.K needs a shout out too. It really struck a chord with me - thinking about things in my past - and i was pretty moved at points.
As for films, i really love Spirited Away, My Neighbor Totoro, Princess Mononoke, and 5 Centimeters Per Second (which needs a UK release!). They're all amazing in their own ways, so i can't really decide.