I haven't watched a whole lot of recent anime(currently only watching Kaiji season 2), but here's a few of my favorites (I'll just ignore the whole "that would be similar to one of these" part
) :
Great Teacher Onizuka
Akagi
Kaiji (it's really slow at points but it's really good)
Detroit Metal City (it's super short but damn funny)
Abenobashi Mahou Shoutengai (Magical Shopping Arcade Abenobashi)
FLCL
Baccano!
Cowboy Bebop
Excel Saga
Tengen Toppa Gurren Lagann
Welcome to the NHK!
I've seen over 300 anime series (yeah, I used to have no life) so I might be missing a few, but those are probably my favorites (ignoring One Piece since that would be way too damn long to watch all of it from the beginning).