Here are my recommendations.
I left stuff off the list if I didn’t see it, or if I didn’t like the way it turned out.

2005
Saishuuheiki Kanojo - Another Love Song (read manga. didn’t see anime)
Angel Heart (good adaptation of manga)

2006
Fate/stay night (differs from the game)
Code Geass Hangyaku no Lelouch (supernatural+strategy+mecha)
Utawarerumono (fantasy + interesting character designs + crappy ending, but still worth seeing for the earlier eps)
Suzumiya Haruhi no Yuuutsu (didn’t see it. heard it was TEH BEST EVAR)
Ray the Animation (*cough*blackjack*cough*)
Saiunkoku Monogatari (spiritual successor to fushigi yuugi?)
Red Garden (heard it was good)

As for your list,
* Black Jack TV (ep 1-30)
got tired half way through.
* Black Jack 21
watched it all. wished for more.
* Honey and Clover (watching, at episode 13)
tired of it.

* Mushishi
skipped
* Black Lagoon
1st ep only
* Blood+
30 eps and quit
* Koukyoushi Hen: Eureka Seven
1st ep and quit
* Ergo Proxy
never tried
* Nodame Cantabile
read manga. assume music is good. no desire to see anime.

Might watch list:

* Kamisama Kazoku
no idea.
* Shakugan no Shana
saw an episode or two. interesting premise, but character interaction feels a bit cliched.
* Le Chevalier D`Eon
no desire to see this.