I'll admit it, my guilty pleasure is Harry Potter fanfic. I don't read any other kind simply because I don't know any other series well enough. I'm obsessed with Hermione, probably because I want to be her, so I generally avoid stories that aren't Hermione!centric and Grangerverse. If you must know, here are my favorite ships:

1) Hermione/Remus - For some reason, HGRL just makes sense to me. I love a Remus who has been shunted aside for most of his life, a little uncomfortable in his own skin, very lonely, and ultimately self-sacrificing. He loves reading, is occasionally mischievous, and adores a certain bookworm Hermione Granger. Unfortunately it seems there aren't many of these fics around. :-/
2) Hermione/Severus - I know this grosses a lot of people out. When I first saw this ship, it grossed me out. But if you really read it, it makes sense. The brightest wizard of his age who has vowed away his life and liberties to end Voldemort and the brightest witch of her age who has been dedicated to the cause since she met Harry Potter? It takes a very dedicated author to write these fics, but good ones are around.
3) Hermione/Draco - I'll admit that Draco is a total git in the books. But if you give him a personality change and close your eyes and pretend he's Tom Felton, these fics are enjoyable.

There are the odd ships that I'll enjoy, ie Hermione/Charlie and Hermione/boy!Blaise, but only if they're written well. I'm very picky about the writing.

What I hate, hate, hate in HG fanfics, in no particular order.

1) Trashing Harry. BIG no no. Harry will always be in my heart. I'm okay with trashing Ron though.
2) Cheating of any kind. I don't like it. Besides Ron cheating on Hermione though... that's completely believable.
3) Drama. God. You'd think that after the war they'd be tired of it. I'm tired of it and I haven't even fought in a war.
4) I'm slightly uncomfortable with trashing the Weasley family in general.
5) Her name is Hermione. Don't call her Mya. Mione is pushing it. And for heaven's sake, even if she turned out to be a pureblood, I can't help but find names like "Gold" or "Evana" completely false. You might as well write a new story and put it on fictionpress. Stop messing with Hermione.
6) Making Hermione pureblood. I've read stories where Hermione is suddenly Blaise's long-lost sister or something... and I hate it. Hermione stands for all the muggleborns who were told they'd never be better than a pureblood. Making her part of a pureblood family just ruins all of that.

What I love in HG fanfics:

1) Mature Harry and Ron. They're ridiculously childish in canon.
2) A softened Severus Snape.
3) A matchmaking Dumbledore. I'm not saying he has to go out of his way to make Hermione "trip" and fall inadvertently on ... Draco or something. But a helpful hint here and there with those twinkling eyes sure makes me happy.
4) Hermione being an animagus.
5) Superpowered Hermione. We all know she was the brightest witch of her age. So why does Harry save the day? I can totally believe that Hermione is the power that the Dark Lord has not...

I think most of what can be said about Grangerverse can be found on pstibbons' profile (google or search on fanfic). I agree with most of her (his?) statements. She's grown out of HHr, which is great. I honestly can't see the two of them together. I'm addicted to Remus/Hermione and Severus/Hermione in the worst way, but I'm running out of credible fics to the point where I'm considering writing my own. Not that I have time at all. I'm very sad that the world of fanfic seems to have died the past few years since it seems I'm a bit late on the uptake and left with all these abandoned WIP. :(

If you happen to be a fellow Grangerverse fan on this site and on my profile, I'd love any recommendations! In addition, I can offer you a few of my own. If you haven't, google ashwinder sycophantic hex for another SSHG archive, Petulant Poetess (I think) for another archive. A great place to go with plenty of SSHG links abound is the SSHG quiz on livejournal. Google that. It'll definitely be worth your while. I know there's Granger Enchanted archives that focus solely on Grangerverse, but I don't really like the format of the site. There are plenty of great fics below that I've favorited, and I would recommend most of them (my tastes have changed over the years though, so beware).

Thanks for visiting!