I honestly don't remember if I've posted in here before, so forgive me if I end up repeating myself in places. Here's some of my personal favorites:
Trigun - A show that heavily influenced me, and I still collect merchandise for it to this day. It caused some friends of mine and I to have a very long conversation on the moral issues it brings up, which to me is the mark of something truly great. I won't go into a lot of detail, as it's a very popular title, but if you haven't seen it I would definitely give it a go.
Master Keaton - This is an excellent, episodic story of a half-Japanese, half-British jack-of-all-trades. Like another of Naoki Urasawa's works, Monster, it's set heavily in Europe and the writing is some of the best you'll find in the manga or anime world. Unfortunately, most will never get to see it, as Pioneer released the DVDs in limited quantities, and they're somewhat expensive these days.
Hajime no Ippo (AKA Fighting Spirit) - This is probably the best shonen anime out there, in my opinion. It's directed by Satoshi Nishimura, of Trigun, with music by Tsuneo Imahori, who also worked on Trigun and provided guitar work for Yoko Kanno on Cowboy Bebop. It's about a teen who helps his single mother with her fishing boat business, but is shy and gets bullied a lot. He's rescued one day by a heavyweight fighter who proceeds to tell him that he has less respect for him than he does for the bullies because he wouldn't stick up for himself, which gives him the push he needs to try and better himself through boxing. The fights are fantastic, and the great thing about it is that you almost never encounter a completely unsympathetic character; meaning you always end up wishing both could win. It's great stuff.
Boogiepop Phantom - This is an awesome, highly atmospheric, supernatural horror story. I love to put this one on around Halloween. The style is very reminiscent of Serial Experiments Lain and Haibane Renmei (which I also highly recommend). I won't say any more, as this is one best experienced for yourself.
Now and Then, Here and There - I forget the Japanese title (maybe something like: Ima, Soku ni Iru Boku), but this is an incredibly harrowing and heartbreaking story of a boy who gets drawn into another world. If you're familiar with Future Boy Conan, it's almost like someone took that and made it a million times darker and more depressing. I know that's not a high selling point for all, but it really is an incredible show. Again, the less known going in, the better.
Planetes - A story about a future where space travel is prevalent and NASA has its own debris collection unit, which turns out to be highly dangerous, yet extremely important work. It's handled with such care and attention to detail that it even became popular with astronauts on the International Space Station.
Please Save My Earth - This is a hard one to find, as it has been out of print almost since Viz released it at the dawn of the DVD era, along with Video Girl Ai (which really tugged at my heartstrings when I was a teen). I absolutely love this six episode OVA. It involves reincarnation, psychic powers, and a bit of a love story thrown in. It's based on the shojo manga of the same name, which is much more readily available than the DVD. The whole thing may be on YouTube, though.
Madoka Magica - This was a recent one for me. I had heard people rant and rave about it, and was like, "What the hell are you people on? This looks like pandering crap." Well, when it ended up on Netflix, I decided to give it a chance, and I finally got what the big deal was. It takes the entire "Magical Girl" genre and flips it on its head. This is another one where it's better if you just see it for yourself. I'll just say that it gets suprisingly dark (like most of my favorite anime series are).
