Most of anime I've seen has been very average, and I've seen lots. Well, actually I sort of stopped following it one or two years back, so I'm no longer up to date. Thankfully I managed to avoid most truly bad ones (not all though...) and find some gems.
I'm a big fan of Yoshitoshi ABe, anything he touches is gold. Haibane Renmei, Texhnolyze and Lain are personal favourites of mine.
Berserk is for me the one and only brilliant action manga. Well, I love 12 Kingdoms, but that's more of a shoujo really.
Cowboy Bebop, Death Note are good ones for those watching anime first time around, they don't contain that many silly quirks. Bebop's even almost episodic, which is a rarity. Monster is a good one too, but 74 EPs might be too much for some.
I loved NGE back when I was 14. I thought it was some deep shit. Then I got older and realised there wasn't any real meaning behind all the random Christian symbols everywhere. Amazing how man people that show suckered in.
Dude, you're my clone.
Same story here really, in fact after second rewatching I strongly disliked it for a while, now I sort of like it. It's a nice middle finger to the otaku fandom.
Last decent anime I watched was The Melancholy of Haruhi Suzumiya. Very funny show.. but you do need a little bit of familiarity with anime conventions to understand all the jokes.
Alright, maybe not, 'cause I hated MHS. I wanted to shoot Haruhi with a shotgun most of the time.