Currently Airing Anime

Haven't seen any of these: - (Impressions from what I've read/heard about them.)

Kanon (2006) - Not my bag
Aria the Animation - Ehhhhhh maybe
ef - a tale of memories. - Not my bag
Kino's Journey - Will add to list, thanks for bringing it up
Lovely Complex - Not my bag
Mushishi - Just started watching this. On episode 6, and it's so... Zen @_@
NANA - Not my bag
Rozen Maiden - Ehhhh maybe
Welcome to the NHK - Tried watching this back when I was very new to anime, and thought it was too slow. I'm gonna try it again and probably like it.

And now, the big ones I haven't seen at all or in their entirety.
Fate/Stay Night - I've tried twice, but usually stall somewhere around ep4 or 5. Don't know why. It's more or less my bag.
Clannad, any of it
Any Gundam/Evangelion
Beck - It's on my list, fear not

 Spoiler

Death Note
I've tried to watch this 3 times, and I make it a bit farther every time. It might just be that I always try again as my anime sprees wind down, or it might just not hold my attention well enough. Which is odd, because I adore shows that try and get into your head.

On the topic of currently airing: If Bakemonogatari 2 isn't subbed by dinner time tomorrow, I'm gonna have to cluelessly watch the raw just to ogle it. @_@

Oi oi, Kanon (2006) and Mushishi are definitely a "big" ones!