I think Harry's eventual ship will probably be clear after HBP. JKR has said that there will be more romance for Harry, and certain hints from her interviews on romance in the books and on her literary tastes make me suspect the next girl Harry likes/dates/kisses/whatever will be the one he forms a lasting relationship with.
Now, I think that if Harry is indeed to have an at least somewhat serious romance as the series draws to a close, JKR had better get a move on with it. As such, I am going on record now as stating my prediction that in HBP Harry will have romantic feelings for a girl that are discernable to the reader. The romance between him and this girl will then come to fruition in book 7.
If what I predict indeed comes to pass, it will be very difficult for any Harry ships besides Harry/ObjectOfHarry'sAffection to keep afloat. So I suspect HBP will be a shipsinker in that regard--one Harry ship will emerge as the obvious front-runner; the others will likely have to resign themselves to being fanon-only after that point.
I predict the winning Harry ship after HBP will be Harry/Ginny. I consider Harry/Luna to be a distant second, Harry/Susan (or perhaps other girls around Harry's age) to be trailing behind those two, and Harry/Hermione to be the most unlikely by far. If, after the 1,000,001 opportunities for H--->Hr to develop, it hasn't yet happened, I think we can safely assume it won't happen in HBP, either. H--->G and H--->Lu haven't had quite so many opportunities, yet those two girls have had a fair amount of development and connection with Harry and his story, so I think it is one of those two that stands the best chance of being the next girl Harry pursues. My favoring of Ginny over Luna is based on her larger presence in the series as a whole, the romantic connotations associated with her character, certain archetypal patterns she better fulfills, my opinion that she is a more suitable partner for Harry in terms of personality and interests, and subtle evidence that Harry seems more inclined to find her attractive.
As for Ron/Hermione, I strongly believe it will sail in canon, probably in HBP, but perhaps not until Book 7. I think there might possibly be some sort of R/Lu on the way to R/Hr, though.
If I am right about both H--->G (or Luna/Susan/etc.) and R/Hr in HBP, then H/Hr would pretty much be definitively sunk after that (at least for canon purposes). In other words, if both those things come to pass, I think the R/Hr vs. H/Hr debate would probably either die out, or turn in to even more of an exercise in futility than it already is--a debate not of which ship will be canon, but of which should be/should have been canon.
What if Harry does like a girl other than Hermione, but there is still no resolution to R/Hr? The H/Hr ship would lose almost as much ground as in the double-whammy scenario. However, they might still stay afloat based on the premise that signs of Hr--->H are still present, and that Harry will have to go through yet another Miss Wrong to find his Miss Right. Something between R/Lu would bolster this position, even if it ended badly between them, because H/Hrs could argue a boy-gets-girl, boy-loses-girl, boy-gets-girl-back (in Book 7) scenario for Ron's romantic subplot. The case for H/Hr would depend, however, on what new clues about Hermione's romantic inclinations arise in HBP. If there is clear evidence (more clear than what R/Hrs have presented as evidence from previous books, anyway) of Hr--->R in HBP, coupled with evidence of Harry--->someone else, it would be hard for H/Hrs to argue in favor of an H/Hr pairing without appearing rather insensitive to their own beloved Harry and Hermione. In other words, it would look a little like, "We love H/Hr so much, we don't care if Harry and Hermione get to be with who they actually want." The ship, then, would depend on arguments that Harry and Hermione's desires for partners other than each other are misguided. As I said before, other Harry ships would also have similar difficulties in staying afloat if Harry develops discernable feelings for a rival partner in HBP. I suspect that if Harry--->Ginny happens in HBP, many H/Lu-ers, and perhaps some H/Hrs (who strike me as being more set in their ways--and understandably so, since they've generally been shipping longer than H/Lu-ers have) would give up the debate. Likewise, I think H--->Lu in HBP would probably deter quite a few H/G-ers and H/Hrs from asserting the canon potential of their respective ships. (Many people will, of course, continue to ship their favorite ship regardless of which way canon goes, but they are much less likely to debate, when it looks like a lost cause as late in the game as after the penultimate book).
But…what if the girl Harry likes in HBP does turn out to be Hermione? (*my R/Hr and H/G shipmates gasp in shock*) We would have a Trio love triangle on our hands, then (since we still have all the clues--generally agreed upon by both ships--of R--->Hr), and I think in that case it would be difficult to predict how it would fall out. In other words, I think that if H--->Hr happens in HBP, the R/Hr vs. H/Hr debate would continue, but on rather different terms. There might be some switching sides for current R/Hrs, though, since many of us have a considerable soft spot for Harry. More definitive signs as to which boy Hermione prefers would be an important factor in which side has the upper hand. Some signs of romance between R/Lu would support arguments for H/Hr as the ultimate resolution of the triangle, and would increase the likelihood of defections from the Good Ship. I seriously doubt Harry will develop romantic feelings for Hermione, however, so I consider this scenario mainly a wild “what if”.
One other possibility I’ve considered is that R/Hr does resolve in HBP, but Harry doesn't show definitive signs of liking another girl. This would leave most Harry ships in virtually the same position as they are now, except for whatever new clues can be garnered from his platonic interactions with the various eligible partners in his life. A given Harry ship may find additional support from signs of [insert girl's name here]--->Harry. H/Hr, however, would face the setback of Hermione being romantically attached to another character. I doubt R/Hr without H--->other girl would be enough to put much of a damper on vocal proponents of this ship, however. Many H/Hrs expected R/Hr to get together in OotP--just like a lot of R/Hrs did--but argued that the pair would still have been inherently unsuitable, and would therefore have broken up before long, clearing the way for H/Hr. The only difference with the same projected scenario occurring in HBP is that there would be less time to come to the predicted H/Hr resolution, but I doubt that most of the H/Hrs that are inclined to debate would consider that a serious obstacle.
Anyway, that covers most of the possible scenarios I’ve considered, and what I think their effects on fandom ship wars might be. As I said, the scenario that I think is most likely is a double-whammy of H--->G plus a relationship between R/Hr, which I think would effectively sink H/Hr, H/Lu, and other rival ships involving these characters. My prediction is that ship wars will be greatly reduced after HBP, and that most supporters of “sunk” ships will either defect (a few) or content themselves with fanon-shipping (most). A few die-hards may still debate, but it will be more about what should happen or should have happened, rather than about what will happen.
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