The Collaborative International Dictionary of English v.0.48:

Swastika \Swas"ti*ka\, Swastica \Swas"ti*ca\, n. [Also
   suastica, svastika, etc.] [Skr. svastika, fr. svasti
   walfare; su well + asti being.]
   A symbol or ornament in the form of a Greek cross with the
   ends of the arms at right angles all in the same direction,
   and each prolonged to the height of the parallel arm of the
   cross. A great many modified forms exist, ogee and volute as
   well as rectilinear, while various decorative designs, as
   Greek fret or meander, are derived from or closely associated
   with it. The swastika is found in remains from the Bronze Age
   in various parts of Europe, esp. at Hissarlik (Troy), and was
   in frequent use as late as the 10th century. It is found in
   ancient Persia, in India, where both Jains and Buddhists used
   (or still use) it as religious symbol, in China and Japan,
   and among Indian tribes of North, Central, and South America.
   It is usually thought to be a charm, talisman, or religious
   token, esp. a sign of good luck or benediction. Max M["u]ller
   distinguished from the swastika, with arms prolonged to the
   right, the suavastika, with arms prolonged to the left, but
   this distinction is not commonly recognized. Other names for
   the swastika are fylfot and gammadion.
   [Webster 1913 Suppl.]

   Note: The swastika with arms bent to the right came to be
         used as a symbol of Aryan supremacy by the Nazi party
         in Germany, 1933 - 1945; hence, it is now associated in
         the United States and European countries with Nazism or
         antisemitism. It is sometimes used by neo-nazis, or by
         antisemites as an antisemitic symbol.
         [PJC]