3x3 Eyes: If more people didn't have a prejudice against 'old' animation then it would be easier to convince them to watch old (awesome) shows like this. This show hold the record for capturing my full attention faster than any other show and it's one of the few shows that I went out and bought, because it was so great. I've yet to see another show (anime or not) where the lead character gets his butt kicked as much, if not more than the villians. Despite being a supernatural show, 3x3 Eyes takes a very realistic approach to the material. Having super powers doesn't mean you know how to use them right away and it definitely shouldn't give you easy win for every fight.
Ayakashi – Japanese Classic Horror ( + Mononoke): Horror anime that is actually scary! As much as I love the Higurashi seres among other horror anime in general- I don't get actually frightened easy by them. But Ayakashi and the spin off Mononoke, achieve what the other series' couldn't. Interesting plot that also leaves me wishing I wasn't watching it alone. In the dark.
Daughter of Twenty Faces: I can't express how happy I am I found this show. I randomly stumbled across it on here one day and I thought it could be something special, but I didn't know just how much I'd end up loving it. It's a cross between FMA and a cozy mystery. I recommend it to everyone and I have yet to have anyone dislike it after I made them watch it.
Ebichu: Another one with iffy animation. I watched this one on youtube and since it's fairly short episodes I ended up marathoning it. Consistently hilarious, perverted, and so wrong it's right. This show is definitely due for a rewatch.
Hare + Guu: Another consistently hilarious watch. I have KiraRin to thank for this recommendation (along with another *HILARIOUS* one on this list). Completely random and chock full of WTF moments that are bound to make you pause it to crack up, Hare + Guu is the perfect show to make you not take yourself (or anything) too seriously.
Hikaru no Go: I don't even know where to start I love this show so much haha. Fairly long show by most standards and I was not bored for a single second. Just hearing one of the OPs sends me into a nostalgic frenzy where I begin to start thinking I can play Go again. Which if internet-go hasn't already proven several hundred times- I cannot play Go at all. Excellent, superb, must-watch shounen. I still can't decide if I like this or Hunter X Hunter more.
Himitsu: The Revelation: The one show I ever found to be a suitable recommendation to the epic Monster. Heart-wrenching at times and downright disturbing at others, this show is not one easily forgotten. I think whether someone ends up liking this show or not- I don't think they would regret watching it, because there's something to be taken from this show.
Hunter X Hunter: Shounen at its best. HxH has all the trademark shounen themes without being overdone or cliche. This show gradually pulled me in and I ended up watching it non-stop. Along with the great OVAs.
Infinite Ryvius: Lord of the Flies... in space! I didn't realize how good this show was until a while after I finished watching it. The characters are real and you can't help but sympathize with them because you'll see yourself in one of them.
Jyu Oh Sei: They could have easily given this show a couple more episodes, but that's not a real complaint. An almost perfect show in my opinion.
Mermaid Forest TV: I know it's definitely not because of the plot, but for some reason whenever I think about this show I get this cozy feeling. Now I wouldn't say this show is scary like Ayakashi or Mononoke, but it has a genuine creepy factor that is not to be underestimated. I can't wait to rewatch this series along with the accompanying OVAs.
Natsume Yuujinchou: Perfect. Natsume and it's sequel are exceptional shows. They have everything you can ask for. Romance, adventure, mystery, interesting creatures, sympathetic characters, heart-warming moments, suspense and so much more. The combination of the music, animation style, and story just struck a chord in me and earned this show a top spot in my favorites.
Platonic Chain: I really didn't want to watch this show haha. I complain all the time about people that wont watch a show because of the animation, but I am guilty of that here. It just looked lame to me. But it's a short show so I gave it a chance and was rewarded. Although it's no where near a favorite, I am glad I bit the bullet on this one. Interesting episodes with stories you wont find in many (if any) other anime. Definitely worth a shot if you like futuristic type stories about youth.
Rose of Versailles: Probably the only show on here I don't plan on rewatching. Don't get me wrong. I love this show. The politics and plots within plots, the huge cast of very real characters, and ongoing suggested romances... I loved it all. I just cared about the characters too much and the drama really got to me. It definitely earned it's spot on my ;_; list here on AP.
Yakitate!! Japan: Funniest anime I've ever seen. I have taken more screenshots of this show than several other shows put together. Just too funny. Everyone should watch this.
Yurumates: Very fun, funny, and cute little slice of life OVA. I don't know why it's not more popular, but if you like that sort of thing you shouldn't definitely check it out.