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Harry, played by Daniel Radcliffe, and Draco, played by Tom Felton, despise each other from the beginning.
After all, Draco's whole family despises Muggle-borns, and they also despise Gryffindors in general. Draco's probably also jealous of Harry for always being in the spotlight and perhaps also for so many people loving him – something Draco sadly lacks, for the most part. Harry mutually hates Draco for being pureblood supremacist and a Slytherin and also for being involved with Death Eaters, as well as for the fact that Draco, out of prejudice and unjust spite, hated Harry first.
But as the years go by, Draco becomes more and more miserable with the Death Eaters, although he continues to hate Harry. After seeing how tortured Draco is, Harry seems to feel sorry for him for the first time. And after Harry saves Draco's life, risking his own in the process, Draco lets go of at least some of his vendetta against Harry – particularly since Harry almost does give his life for others, something Draco observes.
So, although the two are certainly never friends, they at least gain respect and sympathy for each other.