I would suggest it has been, for the vast majority of US history, closer to the "Special Relationship" category than the "Hostile" category.

Its probably fair to say things got pretty hostile around the 1760s, 70s and 80s but other than its been a pretty important relationship on both sides.

British trade laws, for a very long time in colonial America meant that it could only trade with Britain or its dominions. This turned out to be a very good thing for building the American economy, ostensibly because Britain was a pretty big world player in those days.

The were hostilities during the revolutionary phase of America's history but soon after things cooled down again due mainly again to trade but also cultural ties.

Fast forward to the 20th century and you have two enormous world wars, where everything was extremely bleak for a very long time and the US and the UK (and France and Russia) had to work very closely for years to win the wars. This probably had a great deal to do with the modern "special relationship".

Following the wars, the cold war developed which isolated Russia due to its completely different ideological stance (and aggressive foreign policy in some ways indistinguishable from early Nazi foreign policy) coupled with the hang over from WWII, i.e. dealing with the control issue over German territory.

This naturally would drive the other nations closer together as well. Again, trade and cultural ties along with the recognition that they needed to stay friends, drove the friendship. I say they needed to, one because up until the 90's it was a united front against Russia in the cold war (although the US was responsible for most of the antagonism from the western side), and two because well, the cold war shows what happens if the global superpowers don't get along nicely.

Arguably the UK is no longer a global superpower but that's another debate for another thread.

So, as I say, special relationship is the norm. So perhaps the question should be: When and how did the relationship between the United States and Great Britain change from "Special Relationship" to hostile and then swing back again?