I don't follow new anime much, and have only really seen the fairly stock past things - most of the early movies that got releases in the US (Akira, Ninja Scroll, Castle of Cagliostro, that sort of thing...) and the more popular series like Haruhi, Rurouni Kenshin, Lucky Star, K-ON!, Elfen Lied, Death Note, Cowboy Bebop, Trigun...
Manga though... I read LOTS of manga and have a huge follow list at Batoto. Some of my favorites: Non Non Biyori, Spirit Circle, Sora no Otoshimono, Tsuki Tsuki!, Tora Kiss, Rising X Rydeen, Tonari no Seki-kun, Fujimura-kun Mates, D-FRAG!, Hentai Ouji to Warawanai Neko, Rotte no Omocha, Again!, Aku no Hana, Denpa Kyoushi, Echo-pun, Alice in Hell, Tonnura-san, Onisuki, Papakiki, Umi no Misaki.... and literally hundreds more...