Harry and Hermione of the Harry Potter series are excellent friends and nothing more, which is perfectly fine. It would be disingenuous to pair them together since they lack romantic chemistry and have other suitors who fit them better than each other. While these two are not meant to be; J.K. Rowling has revealed that she considered killing off Ron - Hermione's future husband - in the middle of the series. This would have upped the stakes for Harry; however, even if Rowling took away Hermione's partner, the chances of her and Harry ending up together would be slim.
Ron's death would have deeply impacted Harry and the entire Weasley family, but it's unlikely that it would cause Harry to pull away from them, let alone Ginny, his future wife, which means they would likely still have the same end result in terms of their relationship. There is even a chance that Ron's death would have driven Ginny and Harry together sooner with the two of them bonding over shared grief.
The opposite could also be true, with their grief destroying their relationship, but Harry has other suitable options. Many fans ship Harry with Luna since they both remain awestruck by the Wizarding World, share the experience of losing their parents and find each other to be a source of comfort. Luna and Harry are good friends who would compliment and support each other nicely if they chose to be in a romantic relationship instead of a platonic one, and she is just one of several people who would better suit Harry than Hermione, who also has better choices.
During Order of the Phoenix, Hermione reveals that she is still in contact with Viktor Krum, her romantic interest from The Goblet of Fire. These two are a fine pair, and it is reasonable to assume that if things played out differently, they could have ended up together. Hermione likes that Viktor is mature and captivated by her interests as well as the fact that he is emotionally open with her. Meanwhile Viktor admires her intelligence and the fact she does not get star struck around him, even enjoying a simple, leisurely trip to the library with her.
On the other hand, Harry finds this minor outing to be a waste of time. He does not appreciate the extra time in the library and is often bemused but impatient with Hermione's interests that don't line up with his own. In Goblet of Fire, Harry also mentions to Ron during a fight that there's something lacking in his relationship with Hermione that prevents them from becoming more intimate. With a lack of similar interests and inability to be emotionally and physically intimate with each other, these two couldn't make it work as couple.
Furthermore, Hermione is also shipped with Ron's older brother, Fred. If Rowling had killed Ron, perhaps it would have created a domino effect, and Fred would have been allowed to live. This would create an opportunity for Hermione to still officially join the Weasley family but with a different member. More than that, there are a few moments in the books where the two have chemistry, as seen in Half-Blood Prince where Hermione gets a black eye from a boxing telescope, and Fred provides her with an antidote. The scene surprisingly crackles in a way that interactions with Harry and Hermione never seem to do.
Harry and Hermione will always be dear friends. They get along well and push each other in all the right ways; however, they are not destined to be romantically linked, and that is great. Strong platonic relationships are one of the most endearing aspects of the Harry Potter franchise, and it is certainly not a criticism to praise one of the series' leading friendships, even if the two aren't destined to be more than friends.