Some titles that come to mind:

Ah! My Goddess! (classic, charming)
Akira (classic, action, thoughtful)
Arjuna (hippy, thoughtful, poignant)
Bastard! (nostalgic factor - probably not very good)
Bubblegum Crisis (classic, action - new series sucks outright)
Boogiepope Phantom (quirky)
Cowboy Bebop (action - fairly current, easy to get into)
Excel Saga (way, way over the top - only for nUrdy anime fans)
FLCL (quirky, comedic)
Ghost in the Shell (action, sci-fi, semi-thoughtful)
Grave of the Fireflies (classic, thoughtful, poignant)
Haibane Renmae (thoughtful, charming)
Heat Guy J (poor man's Cowboy Bebop)
Hellsing (shallow, action/gothic type)
Jin-Roh (thoughtful, dramatic)
Last Exile (action, charming - current release)
Magical Shopping Arcade Abenobashi (comedy/quirky/thoughtful)
Najica Blitz Tactics (only funny for being so wrong)
Neon Genesis Evangelio (my personal favorite - long live Ayanami)
Princess Mononoke (action, thoughtful, poignant)
Record of Lodoss War (classic, action, fantastical)
Serial Experiments: Lain (quirky, thoughtful)
Spirited Away (charming)
Trigun (action)
Totoro (youthful, charming - current DVD sucks, Disney DVD will be better)
Vampire Hunter D (classic, action, gothic)

Otherwise, a lot of it is subjective to personal tastest and/or nostalgia. I never watched Robotech much as a kid and, looking at it now, I cannot help but think of how badly it sucks (much like how I love Tron from way back when, but my friends and associates wonder what in the heck I am talking about.)

There are a lot of good, yet not great or semi-generic releases, too. This would cover anything from the Love Hinas to the Gundams and everything in between. There are many more eclectic titles as well - things like Cat Soup or Doggy Poo.

Currently, nothing is blowing me away. I am really enjoying Last Exile, but I would not consider it great. I am eagerly awaiting Wolf's Rain; I am hoping it is as good as it seems it could be. Alternately, I love the original Ghost in the Shell and am looking forward to, when it is released, Innocence and, late next month, the release of Ghost in the Shell: Standalone Complex. Otherwise, I am really enjoying the pointlessness of Azumanga Daioh.

I cannot think of the name offhand...but I want to check out the one with the alien frog commander that is stranded on Earth. I do enjoy Big O, both series, but I cannot honestly tell you that it is a good series - I keep on hoping the story will be better than it is and I do have a fondness for the mixture of the former animated Batman series and anime.

Give Cowboy Bebop a whirl, though - it is really good and would be very easy to get into based upon its action and coolness content. Akira is a great classic and I absolutely love Neon Genesis Evangelion, but it may be a bit heavy for a new anime fan.

Incredibly let down by Witch Hunter Robin,
Ray

Edit: Added one title.
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This comment was edited on Jun 24, 05:51.