In general I don't much care about pairings so long as they are believable. That said I disliked the pairings given in the Harry Potter books and do not believe they were portrayed well. I absolutely loath Hermione and Ron as a couple which is very unusual for me (don't really care about Ginny/Harry though I do think it could have been shown better in the books). The pairing I like the most and would have preferred is Hermione with Harry and there are various parts of the books that support this pairing even though it is not one of the official pairings.
I do not hate that Harry ended up with Ginny but do not feel that the books made the pairing believable. I don't like various aspects of it like how she had been infatuated about Harry even before meeting him (she was a fan girl that wanted him without knowing him at all), how she went from a person Harry barely noticed or talked to, to being his love interest so abruptly, the introduction of love potions at around that point in the story and the earlier mention that Molly Weasley had made love potions in her youth (why would any school teach teenagers how to make love potions or keep them in the school anyways seems like a recipe for disaster to me - also while it is said that love potions can not create love they can cause infatuation which can lead to love and might be able to change a budding romantic love into a familial love since the person under the effects of the love potion would have more physical reactions to the person that gave the potions than a person in which he or she is just starting to see as a potential mate; having him discover/fall for Ginny right when love potions were introduced was a poor decision in my opinion), feel more like he was lusting over her rather than in love with her, and other reasons.
While I don't particularly like the Ginny/Harry pairing (for some of the above mentioned reasons amongst other less rational reasons); I really don't like the Ron/Hermione pairing, I loath it. Having them date or shag I could see happening but don't think that they make a good couple at all (and this is not only because I prefer Harry/Hermione). I much would prefer that she be with someone else (saw a couple fics that had her be with Luna and found that to be an interesting though unlikely pairing). Without Harry Potter being there I find it highly likely that Ron and Hermione would have had nothing to do with one another at all possibly even becoming entirely hostile to one another. They also have very few common interests and both pretty much dislike to a significant degree the others most valued hobbies (she likes reading he doesn't, she views studying to be important he doesn't, he loves chess and quiditch she doesn't, he's lazy she's hard working, etc.). I really did not like that Ron got a book about charming witches like the love potion mentioned for Ginny the book makes me feel that Ron is changing his personality to get Hermione instead of doing so to improve himself that he was manipulating her. The way I saw it in the books was that Harry needed Hermione and she needed him while both care for Ron he is much less important to both of them and I know for a fact that I'm not the only person to view it that way.
Whether Rowling meant to or not she did include a lot that made me think of Harry/Hermione rather than the official couplings and included things that led me to doubt the official pairings. Harry and Hermione no matter how you look at it are shown to care for one another very strongly much more strongly than what I believe a brother/sister relationship is (and I have a brother and sisters) and get along much easier and believably than the official pairings do. I could write many reasons as to why I like this couple but don't feel like it at this time. If you want to read essays showing why Harry/Hermione make a good couple and scenes from the books supporting this pairing you can go to portkey.org and find on the forum some very good essays that show why they make a good couple using evidence from the books (I haven't seen a very persuasive argument for Harry/Ginny since the ones I did see pretty much come down to that's how J K Rowling wrote it). Even J K Rowling admits that the potential was there and that they had charged moments.
A fanon theory that I like was that Hermione believed Harry was in love with Ginny (rather than in lust which is my take on it) so she decided that Harry was taken so did not try to pursue him and decided to like Ron since he seemed to like her and she does have some feelings for him (she does consider him a friend and friendships can lead to love) even if he is a jerk to her on occasion (he makes her cry and upsets her too damn often in my opinion). As for Harry, he never seemed to be very happy with his two best friends becoming more than friends in the books but he was in lust with Ginny at the time and for teenagers especially it is easy to mistake lust for love (which doesn't mean that he didn't eventually actually fall in love with Ginny).
Tonks/Remus pairing. I have no real reason to not like this pairing it simply doesn't seem like a good pairing to me (though Lupin being quite a bit older than Tonks maybe part of it). I also dislike that both of these characters are killed off leaving an orphan. I heard that originally Arthur Weasley was supposed to be killed off by Voldemort's snake but J K Rowling changed her mind and instead decided to kill these two characters off instead which if true saddens me. Tonks and Remus were both more interesting characters than Arthur and in my opinion it’s much sadder for them to die. While not a pairing I like, I dislike that they died shortly after having found love leaving a child orphaned. Arthur is much older and had a longer and/or more fulfilling life than Tonks and Lupin. His children were all of an age in which they could have dealt with his demise and it would give Ron or Ginny a real tangible reason for revenge as well as allowing for more believable character growth for the Weasley family.
As for fan fiction ships, while I prefer Harry and Hermione (because I am convinced based on the books and movies that is the best match up in the series) I have read fics with other pairings including Ginny/Harry that I found to be much better and far more believable than how that pairing was displayed in the books. I'm okay with most pairings depending on the skill of the writer but seeing Ron and Hermione as a couple in a fic spoils the fic for me. The story could be otherwise good but I dislike that pairing so much, to an irrational degree, that it can turn an otherwise good fic into something I can't bring myself to continue reading. I really would like a warning that Ron/Hermione is a pairing in fan fics.