Sadly I haven't watched a lot of Anime nor finished reading any Manga/visual novel series. However some have clawed their way into my notice:
Anime
The only ones I've seen from start to finish are:
Digimon (Season 1+2+3), watched a bit of 4+5 but they weren't as good in my opinion (the Japanese version of 5 had some promise though)
Deathnote
Yep that's it, the others I've seen bits of are:
Pokemon, oviously everyone knows what this is
I never really got into the Anime though, the first movie was ok.
Monster, saw the first five episodes in Japanese and loved it (I saw them on YouTube I believe)
Mushishi, same as Monster
Sailor Moon, too young to remember any of it now though (except that opening theme pops in my head sometimes)
Manga/Visual novels
I've read some of:
Deathnote
Digimon Next
Darren Shan
And that's it from me on this rather nipongo themed post sayonara