Recommendations

In both Clamploo and Black Cat, individuals capable of holding their own groups together and travel together. Sometimes their styles can coexist other times they seem to bump heads.

Both of these harem anime highlight their attractive character designs by incorporating lots of fanservice. Also both are light and fun viewings, complete with girls who have an obvious brother complex.

Both have a girl with long white hair which suddenly appears out of nowhere and follows the main character.
But the big difference is that Ano Hana is more focused on drama and friendship when Deadman wonderland has more of a gore and psychological type of story.

Sora no Otoshimono is like Henneko because:

1 Main Character:
In both series the main characters are somewhat perverted but are really nice.

2 Main Heroin:
Main heroins are unemotional

The protagonist, who is far too kind (kinda negative), teams up with someone strong to defeat enemies. Both are male and have a popular female fellow student as a partner who teaches him new things.
Accel World and the Holy Grail War are both settings in which the main characters have to fight and win to gain something.

Both "Paprika" and "Perfect Blue" have quite deep symbolism and surrealism.
However "Paprika" is much more higher all the way and in any aspect, in my opinion.
I like how "Paprika" concentrates in itself all of Satoshi Kon favorite images and themes:
1) Like an escape from reality into a world of illusion
2) The devastating consequences of the invasion of illusion into reality and getting rid of these illusions
3) The sudden realization that the difficulties can be overcome, but turned to face them
4) Detective story filled with riddles and symbols
5) Surrealist paintings of collective and individual insanity
6) Adult man tired and lost in his past
7) Young woman who live a double life and hiding from all its second, the internal and true "I".

But I think Satoshi Kon described these all themes best right here in "Paprika" (that's his last finished work, by the way, before he is gone). In my opinion this is his best work after all.
Frankly saying, I don't like "Perfect Blue". I really liked "Paprika" much more. So, maybe if you don't like "Perfect Blue" too, try this one, I think you will not be disappointed. That's quite for sure.
Moreover there are great qualitative soundtrack, beautiful and detailed, outstanding animation.

P.S. Sorry for not very good english, it's my third learned. But I hope my recommendation will help somebody.

Same sort of characters and same sort of comedy. The setting between the feudal era/modern society is similar too. The only difference is that it moves a lot faster.

They both are really funny anime to watch. There isn't a big story in it, so it's easy to follow; you could watch episodes randomly because there isn't really a line in it, but there is so much comedy in both!

Both Kara no Kyoukai series and Denpa Teki na Kanojo gives similar dark, interesting and tightening feel with a some romance in it.
Both have female leads quite similar to each other.
If you liked one you should try another.

Boogiepop Phantom and the Demon Prince Enma are horrors with very dark, twisted, and surprising story. The main character Enma reminded me a little bit Boogiepop also both shows show us the real human nature. If you liked one you should see the other.

Mondaiji-tachi ga Isekai kara Kuru Sou Desu yo? is more serious than Dog Days, but they both include characters being called to a fantasy-like world by a female with animal qualities. The summoned "heroes" are then asked to aid the summoner with protecting their world or their country. In order to do this, the heroes must fight through games/competitions. If you liked one you may like another.