Alrighty, now I have some time. Anywhoo, almost 
all of the above anime are new (the oldest listed 
is Saiyuki, which ran on TV from 2000-2001), and 
so a nice fresh look at the state of anime in 
Japan today. However, the character designs are 
all starting to look cut and paste, and te 
detailing in digital anime is minimal at best. 
Frankly, digital animation has a long way to go. 
Saiyuki, for instance, is physially painul to 
watch at times, but because I love the story and 
charactes so much, and seeing how the series 
differs from the manga (the divergence occurs in 
season 2), keeps me going. Final Fantasy 
Unlimited, Angelic Layer...anime such as these 
look rather flat to me, as cute as they are. 
Fruits basket has that same flat look, but they 
do such different things with it that I just 
ADORE this series. I heavily recommend Fruits 
Basket :D

Now, if you want good older anime, there's the 
classic Lodoss saga, and there's Catgirl Nuku 
Nuku, Lupin III (a classic! Good family fun, if 
family fun were lecherous and horny :D), Toward 
the Terra (it should be no small clue to everyone 
how much I adore THIS series, the ORIGINAl 
Macross saga, etc. There are about a gajillion 
OAV's, as the late 80's and early 90's saw an OAV 
boom.
Of course, anime gos back much farther than that, 
and I encourage you to delve into the wonderful 
anime that brought us to where we are today.

Then, of course, there's the stuff that is not 
old or new, but for the time being, just kinda 
exists...such as Tenshi ni Narumon(1999), 
Violinist of Hameln, Gundam Wing, Inu Yasha 
(started running in 2000), Irresponsible Captain 
Tylor, etc. 

If youw ant ideas or suggestions, visiting 
www.fansubs.net and checking out their titles 
list may help ^_^ Here's a link to said list 
(note that no all of these are still distributed 
by distros, this is merely a list of everything 
that has, is, and will be):

http://www.fansubs.net/fsd/index_l1_0.html

Hope this helps!

-Misha