I guess I don't exactly insist on dubs. Just give me something good, I'm sure subtitles wouldn't bother me.
Well, how about my Top 5:
5) The Melancholy of Haruhi Suzumiya
Dub Quality: Meh
The Melancholy of Haruhi Suzumiya is a sort of sci-fi/romance/comedy anime about a high school girl who is obsessed with the supernatural. The first thing she says to her classmates is "If anyone in this class is an alien, time traveler, esper, or slider, come talk to me, otherwise, don't bother." The protagonist then unwittingly convinces her to create a club to investigate the supernatural.
4) Elfen Lied
Dub Quality: Awful
You've seen it, I think. Moving on...
3) Bakemonogatari (translates sort of as MonStory or GhoStory...bakemono=monster, monogatari=story)
Dub quality: Non-existant
Bakemonogatari is about a high school boy who is a former vampire. The format of the show is that there are 5 arcs, each arc focusing on a girl. In each arc, the girl in question is being tormented in some way by some variety of animal-based demon. With the help of a sort of supernatural detective guy who helped cure him of vampirism, he helps these girls with their respective demons. Despite how it may sound that's not really what the show's ABOUT...it's like 75% dialogue, and 50% of that is just banter. It's extremely entertaining and rather romantic, and I love it.
2) Kara no Kyoukai (Boundary of Emptiness)
Dub quality: Non-existant
Kara no Kyoukai is about a woman named Ryougi Shiki. Shiki has an ability called "Mystic Eyes of Death Perception", which allows her to see the 'deaths' of people and objects. These manifest as lines. If she cuts someone/thing along these lines they will be killed and/or destroyed. She works for a woman named Aozaki Touko who has her fight supernatural stuff. There's a lot more to it than that but if I get any more detailed it will be spoilers. Let's just say a lot of mindfuck and badassery.
1) Higurashi no Naku Koro Ni (When the Cicada Cries)
Dub quality: Awful, and iirc incomplete
Higurashi is about a young man who moves to a small rural village with his family, and things are not exactly as they seem. I honestly can't get into more detail than that because I would spoil something. Suffice it to say that everything this show sets out to do (except for the animation, which is horrifically bad in the first season, but then gets a little better as it goes on), be it comedy, horror, or tragedy, it does perfectly and extremely effectively. Great characters, great plot, all around great. Can't recommend enough.
Go watch Baccano. Has comedy, action, and a pretty intersting story/storyline. Its fun keeping track of what episode youre watching
Baccano! is also an excellent recommendation, top 20 show for me.
Also, here is a list of pretty much every anime I have ever seen and what rating /10 I would give it:
https://myanimelist.net/animelist/genowyn