Here are some general things I like:
(by no means an obligation or a checklist)
I like humor.
I love plots.
I love folklore and working off of mythologies and urban legends.
I love examining the relationships between people (though I'm not generally a fan of romance or porn, except where explicitly noted)
I like math and science, especially when taken to the brink of implausibility
I have a weakness for puns.
I like politicking and murder mysteries and conspiracies and complicated plots, but these are hard and would be totally beyond the call of duty.
Did I mention I like humor? Because a touch of humor in any story is awesome, even if it's a tragedy.
I like a little grain of discomfort/unease mixed into otherwise pleasant stories.
I like a strong sense of setting or culture
I like a sense of impending disaster.
I like it when an author's love for the characters and story really shows.
Here are some things I'm not really into:
Porn and stories that are all about romance. This does have some exceptions--I think Yuta's budding relationship with Keiko is adorable, I'm fine with giving Saint Walker a family or partner in the past (or ship him with Mogo--that'd be really interesting!), and Razer/Aya is really cute. But, for the most part, I'd like these to be kept at relatively the same level they are in canon.
Characters being unpleasant to each other all of the time (fine in small amounts and fine if it's in character, but too much of it starts to get me down)
Character bashing. Believe it or not, there are very few characters in these series that I don't like. (And if you don't like a character, it's okay for you to not write them! Seriously, I understand! Do what you love, not what you hate!)
Introspective stories that don't have things happening. I like things to happen. They don't have to be big things, just. Something beyond just thinking.
Stories that work at a different emotional level than the source material. Dark humor is great for Kurosagi Corpse Delivery, but not so much for Green Lantern or Journey. Even though a lot of the canon I chose has something dark or tragic in it, I think they all have a bit of hope in it as well--the Journey goes on, Yata and Norman find people who understand and believe them and, well, the entirety of Saint Walker's storyline. That's what I find appealing about all of them, so even if your story is sad or tragic or dark, I like the sense that there's the possibility of things growing better.
ParaNorman (2012)
Norman Babcock
My favorite part of the movie was Norman's friendship with all the ghosts, how friendly and happy he seemed when he spoke with them. I'd love a story that deals with that sort of day-to-day interaction, how the ghosts are just a normal part of his life, even if nobody else can see them. I also love his growing closeness with his family and Neil, and how he's learning to balance his paranormal life with his normal life. I'm also a sucker for a good, old-fashioned ghost story, and a bit of creepiness is always appreciated, so take that however you like. (Also, since I know this is a "thing" in some groups, if you want to do a crossover with any of the other Spooky Kids movies/shows such as Coraline, Gravity Falls, etc., I think those are also wonderful and have the potential to be really fun)
Journey (Video Games)
I love this game, so anything that has the same feel as it would be delightful. Each time I played it, the interactions with the other people I came across made it a new experience, and the ways we all acted made it a different story every time. If you'd like to narrate one of your Journeys, I'd love to hear what your story was like. Or you can delve into the mythology, or take the Journeyfolk on a new adventure. After all, I imagine they tend to get sidetracked and lost on a fairly frequent basis.
Green Lantern: The Animated Series
Saint Walker
I love how wonderful and loving and silly Saint Walker is, and how he's been through so much pain but still believes that everything will ultimately be good. His interactions with Razer were hilarious, and his relationship with Mogo is fascinating. Some pastfic would be interesting--what happened to his planet, how did he earn the "Saint" title, how did he end up on Mogo after the disaster--or a story where A Planet and his Blue Powerup go out and do spacecop things would also be terrific. Or ultimately, if you prefer, I ship Razer/Aya pretty strongly, so you could always give me some cute fluff about them. I'm pretty easy that way. (I'm only passingly familiar with the comic, so while you can draw inspiration from it and I am familiar with the main characters and events, I'd prefer it if you stick largely to the Animated universe)
Kurosagi Shitai Takuhaibin | Kurosagi Corpse Delivery Service
Yata Yuji
I have this bizarre fascination for this creepy, dark, yet often touching and funny manga. Yata and Kereellis are my favorite pair out of the bunch (though Yata's budding relationship with Keiko is also very sweet). Something starring Yata and his alien-possessed hand puppet that has the same feel as the manga would be great. A casefic would be wonderful, or something where Kere'ellis gets to save the day (or perhaps Yata gets to save him for a change?), or a moment where one of them gets to bond with someone else in the cast. Feel free to go as creepy as you like with this--I'm a little squeamish when it comes to some things, but for some reason, I have a big tolerance when it's related to Kurosagi Corpse Delivery.