Shown here are some usages of the swastika from, top to bottom: Finland(municipal coat-of-arms), Japan (municipal flag), India (provincial seal), and Korea (Buddhist temple). 7,000 year old swastikas have been found in the archaeological record. According to Wikipedia:
The word swastika is derived from the Sanskrit word svastika (in Devanagari, स्वस्तिक), meaning any lucky or auspicious object, and in particular a mark made on persons and things to denote good luck. It is composed of su- (cognate with Greek ευ-, eu-), meaning "good, well" and asti, a verbal abstract to the root as "to be" (cognate with the Romance copula, coming ultimately from the Proto-Indo-European root *h1es-); svasti thus means "well-being." The suffix -ka either forms a diminutive or intensifies the verbal meaning, and svastika might thus be translated literally as "that which is associated with well-being," corresponding to "lucky charm" or "thing that is auspicious."
Of course, the swastika has come to be associated with something entirely different in modern times - but, as the examples here illustrate, this has not obliterated its older senses and uses. The last photo is one I personally took, and I can testify from personal experience that it is a common symbol in Buddhist architecture in Korea, with no negative connotations in that society.
Two interesting facts: 1) that a symbol can come to have two diametrically associated meanings/connotations; 2) that people aware of one meaning can be utterly unaware of the other. I bring this up in the context of recent news stories surrounding a little girl involved in a custody case in Winnipeg. Apparently, her parents belong to some kind of neo-Nazi organization (or perhaps would like to), and the court case stems from, among other things, her being sent to school with swastikas and other markings drawn on her skin. Nowhere have I seen any mention that the swastika has any other association than with Naziism.