Things I generally like in stories: I've been reading fanfic of various sorts for the last 20 years (and writing a bit, too), so I think I've tried about every genre and type... and I have to say, I enjoy most of them. Actually, it depends on my mood -- sometimes I am really not in the mood for thinky fics or for romance, but soon enough I'm going back to them. A decent overview of what I like in my fanfic can probably be found in my various bookmarks and recommendations. I used to maintain a rec journal at spacedoc, but now I just usually bookmark things on AO3. That'll give you a rough idea, anyway.
I'm a big fan of slash stories, but I also really enjoy het, gen, or femslash. I enjoy the emotional side of stories along with actual plot (mystery, casefic, etc). There are a couple of tropes that I particularly like, so I'll list them here.
1. Outsider POV - What I mean by this is that the story is being told from the point of view of an unreliable narrator who doesn't fully understand what is going on and makes assumptions based on the evidence they can see. As the reader, I know more about what is really going on and the dichotomy between that knowledge and the perfectly valid evidence of the narrator is delicious. (Example: Mr. Spock is a faerie-angel because he appears in a shimmer of light to a little girl on an alien planet that doesn't even understand the existence of other worlds, so she believes he's going to grant her three wishes if she feeds him a gngxlytsi flower. Spock, meanwhile, is after a bunch of what we recognize are Romulan pirates, but the little girl thinks they're demons. Example: Duncan MacLeod is obviously a super secret spy/assassin/ninja according to Detective Randomchick, because look at his file! Look at the evidence! Look at those abs! What else could he possibly be, what with all the shady people watching him and his traveling all over the world and the multiple strange encounters that she half-understands, right?)
2. Culture Clashes - This may or may not tie into the above, although they work well together. When one character is having a really hard time understanding another but eventually learns how to think like they do or understand their point-of-view, even if it is so incredibly out of their own comfort zone and foreign that it twists up their brain a bit, I just love it. This can be done very poorly or very well in fic, so tread on it at your own risk. This can be written using all sorts of clashes, like 1st World versus 3rd World, socioeconomic hierarchy, ethnicity/race, disability, sexuality, etc. I always squirm a bit in my seat over cultural misconceptions and negative prejudices, but I usually enjoy the resolution of the story when a character has an epiphany and starts understanding, or even just trying to see the world in a different way. (Example: Just about every Stargate episode, in a creepy imperialistic way, albeit still fun. Example: Fraser and Vecchio's Northwest Territories, Canada, versus Chicago, U.S.A., banter on Due South and any story that explored the differences and similarities between the two as part of an Odd Couple motif.)
3. Crossovers/Alternate Universes - I LOVE LOVE LOVE crossover stories. I'll even read crossovers between fandoms that I don't know much about, I love them so much. I think I like them so much because of the same reasons I enjoy the previous 2 types of stories -- outsiders getting to know each other, cultural misunderstandings and clashes between strangers, and secrets. I adore crossover stories where a character from one fandom is inserted into another fandom, particularly if the character is running away from his/her past and is keeping secrets from the people they are involved with now -- and of course, the people in the new place are trying to discover everything they can. Angst and pathos, yay! (Example: Martha Jones of Doctor Who fame finds herself working for MI-5 (ala the show Spooks) and trying to keep secrets from people whose job it is to uncover secrets is rough. Can she do it? Or, if she gives herself away as a time-traveller and companion of an alien, will they ever trust her?)
I'm also fond of AUs, either minor or extreme, but it's always the characters that draw me in. Specific AU-types that I enjoy are paranormal (magic-users or everyone-has-superpowers or fairies or vampires, etc), the daemons of Phillip Pullman's His Dark Materials series (although I didn't like the books so much, I LOVE the concept of everyone wearing their soul as an animal), BDSM universes, heat/fuck-or-die universes, secret societies and conspiracies, Sentinel-AUs (based on the 90's TV show), AUs in which one character is secretly evil and/or on the other side than in canon, space opera AUs, whoops-my-mother-is-an-actual-Greek-godd
Things I generally do NOT like in stories: This list is ever-shrinking, because inevitably someone writes a story using a trope or genre I think that I totally hate that is actually amazing. This has happened to me. A lot. Still, there are a few things that generally bother me in stories. I don't have any triggers, per se, but there are things I don't like.
1. Hate = Love - I really dislike stories where characters who are truly portrayed as hating each other in canon or who are ultimate enemies get together somehow in fic. Now, this can be done well if the author builds it slowly or does a complete AU of the canon, but seriously, just because people fight each other with furious passion does not mean they should be fucking each other with furious passion. (Example: Harry Potter/Draco Malfoy, ick ick ick. Example: Batman/Joker is just too brain-breaking for me to contemplate, based on decades of canon, no matter how hot the two actors playing them in the recent movies are.) That said... sometimes it works for me, I don't know. *shrugs*
2. Babyfic - Again, I have read some amazing kidfic and even recommended it, but I'm not generally fond of stories about raising children. This is possibly because I don't have any of my own and don't ever want any. Don't get me wrong, I like kids -- kinda have to with my job -- but I just don't find the minutia of raising one or more particularly fascinating. A subset of this is pregnancy (or mpreg) fic. I've read some I've enjoyed, but it'll never be something I go searching for specifically.
3. Torture Porn - I'm a fan of Hurt/Comfort, but sometimes a story will go too far for me to enjoy. When a story devolves into non-stop pain for one of the main characters, with every detail lovingly laid out to the reader, I simply can't abide it. The torture can be either physical, emotional, or spiritual, it doesn't matter. I'm not talking a scene or even a series of events described in-depth, I'm talking about when a story just drags on and on while lingering over the torture without resolution. I once got really involved in a looooooong Doctor Who fic where horrible things kept happening to the Doctor and yes his friends were there to take care of him each time, but it was too much and I had to give up reading it even though it was very well written. I understand that writers often hurt the characters they love most, but I can't take it when it goes on too long or doesn't have a resolution. I'll read torture, abuse, or rape-aftermath stories, but not gratuitous ones and they'll never be my favorites.
Whew! That was a lot of writing and thinking about what I like in fic. I've probably missed something, but I've allowed anonymous comments for this post, so if you have questions, sweet Yuletide writer, go for it. Also, thank you for writing a story for me! :D
PS: Here is a link to my requests and offers.