Go for Deathnote, it's one of those ingenious things that you won't want to stop watching.
2nd recommendations,
Ghost Hunt is great even though it is not made up of a single story line but rather short arcs. I really enjoyed that one.
Shakugan no Shana, although it has slow points i personally found it to be memorable, very rare among so many animes out there.
Gun x Sword wasn't entirely original in plot, but i found it enormously enjoyable.
Claymore, very cool, but also very current, only 4 episodes out.
Kanazuki no Miko - not popular, some people might trash it, but IMO i loved that series definetly one of my favorites, and a very original plot and style. The sound track kicked butt too.
Full Metal Panic is not super duper original but its got a great plot and is certainly one of the most watchable animes ever.
Darker than Black - also looks spectacular, but only about 4 episodes subbs do far.
What *not* to watch:
Erementar Gerad, Black Cat, Jigoku Shoujo, Tsubasa Chronicles
these seem popular but im luke-warm to them:
Fate/Stay Night - Good anime, fairly flat plot originality
Speed Grapher was certainly original, but i found parts of it sequential, and rather unsatisfying in general.
You may want to get recommendations on these, i plan to see them but have not yet, they look very good:
Mushishi
Basilisk
Gilgamesh
Bakumatsu Kikansetsu Irohanihoheto