I will provide explanations as long as I don't get bored of providing them.
1. Neon Genesis Evangelion
Okay, the big one that has gotten me back into 90's anime. It's got giant robots, fanservice, psychological WTFery, hot flaming characters, near blatant yaoi, violence, science fiction, theological allusions "thrown in for flavor," about ten different kinds of Oedipal complex... Put simply, it's got everything. The only thing that sucked had to have been the ending, as there's just no way to end a series like this properly (although End of Evangelion did so fairly okay).
2. Trigun
Steampunk anime with hot blonde with such an interesting character. Even though it's a short series, all of the main characters get so much attention and therefore plenty o' dimension to them. The plot is fascinating, and the philosophy actually makes you think.
3. Spiral ~ Suiri no Kizuna ~
It has a nice pace, beautiful art, catchy themes, and a plot that kept me glued to the screen. It's a lot like Sherlock Holmes meets anime, only without the goofy aspects of Case Closed (which has its own good points). It's dark, it's exciting, and it generates plot bunnies. Yes, even considering the ending.
4. Alien Nine
Although it leaves a lot of questions (both in the anime and the manga), it's still awesome because of the deception. Just from looking at it at a glance, one would think that it's just a cutesy anime about a bunch of elementary school girls. But then, one of the girls' symbiotic partners brutally kills a parasitic alien, and it shows the blood and gore in great detail. From then on, Alien Nine takes on a fast-paced, eccentric web of (possibly psychological) mayhem that ends on a dramatic note in both versions that leaves a lot up to interpretation.
5. Pokemon, first season only
It has to be the first season, as everything else lost its touch, I think. The first season had a certain magic to it, possibly embodied by the fact that it had piss-poor animation framed by really awesome storylines that tried to get away with so much.
6. Sailormoon
I don't usually like cheesy magical girl anime, but because this was also the first anime series I've ever seen, it holds a certain nostalgia. And, well, the fact that it had that very 90's quality to it somehow elevates its awesomeness. Or maybe it's just because the idea of planetary soldiers is just that cool.
7. Jigoku Sensei Nube
I can't quite decide if this show is taking the entire exorcist genre seriously or not, given the fact that its fight scenes tend to be serious, whereas everything else... not so much. Either way, Nube is awesome, the fight scenes are awesome, the demons are awesome, and the humor is not only awesome but also incredibly perverted. Who knew elementary school children could be so dirty?
8. Elfen Lied
Bloody, psychological, reminds me of Chobits if Chii went homicidal. I think we should be setting up a pattern here.
9. Witchblade
Other than the fact that I think the Witchblade concept itself is really cool (even in Western media), this anime is beautiful on so many levels, including the mother-daughter drama as well as just the images. And, oh yes. Plenty of fanservice.
10. Ouran High Host Club
I admit it. I watch it just for Tamaki.