Death Note is really the only anime I've ever been able to enjoy start-to-finish. An ex-gf showed me 'Gurren Lagen' or some-such which I thought was okay until the comedy, the only decent part of the series, suddenly disappears with the death of a specific character (older brother if I recall correctly?) and it suddenly tries a complete tone shift to grimdark seriousness. Fucking killed it for me.
Oh, and she showed me Code Geass, which was definitely watchable and has a neat story. Too much pointless mech shit though (not relevant to the plot and seemingly just to pad the episode count, I should specify).
I'm open to any suggestions along the lines of Death Note, I loved the battle of wits that played out throughout that one.