After the publication of Hitler's Mein Kampf (my struggle) the swastika became popularised and politically recognised with the Nazi party in 1920's. The symbol was already being used in Germany at the time, but without the obvious genocidal connotations, it was merely seen as a symbol for creating, normally associated with working class parties. And although the Nazi party had strong ties with socialist ideologies, this is unlikely to explain Hitler's choice. There was however a theory prevalent at the time, of their Aryan cultural descent, believing that they descended from an earlier, racially pure, white population. Becoming obsessed with their Nordic ancestry, the swastika was a symbol of that imagined master race; a no brainer I suppose, from a seriously sinister perspective.
Hindu's for example far from viewing it as negative see such a symbol as a means of good fortune of auspiciousness, and have used it in this manner for thousands of years, representing one of the 108 symbols of their god Vishnu. It's widely used, adorning all their temples and architecture, even their art; hell it's even used as an essential part of wedding ceremonies, as a blessing to their union, ensuring good fortune.
Buddhism is also no stranger to this mysterious symbol, for followers of this faith it is synonymous with the footprints and the very heart of the Buddha himself. Now it's worth bearing in mind that we may view feet here very differently here in the west. Far from being a sight of disgust or sometimes horror, feet are deeply interconnected with that of respect, as feet themselves are symbolic of progress and Buddha's presence in our world. So rightly so they are revered, which should give you a level of keen appreciation for what this symbol would represent.
Here are some other examples of it appearing in other cultures all over the world
(right-Roman Vila, left-Church in Ethiopia)
Finally, why do you think it appears so universally? Across such expansive epoch's, with people's that had little or no contact with one another. I would argue that in this case Carl Jung had it right, he theorised that there was a duality to human consciousness. Firstly you have your immediate consciousness which contains our personal nature, thoughts, and the aspects of our individuality.
Then running parallel to that is the 'collective unconscious' which is a repository of knowledge, of universally shared symbols and meanings, that are understood by all, and are completely innate within us. These pre-existing forms are called archetypes, a mental version of an instinct, examples of this motif would be concepts like the serpent or the devil, concepts that are passed down genetically from one generation to another.
Thanks for reading.http://www.religionfacts.com/hinduism/symbols/swastika.htm