Before we get over ourselves (structuralism in mathematics? game theory? please), I'd point out the simple things:

• The deductive method (some Greek did it, most likely not Euclid). The basis of everything;

• Logic (from Aristotle onward). The basis of almost everything;

• The indo-arabic Decimal (and positional) system, which vastly increased computational capabilities and ways to think about quantities (including logarithms and the concept of order of magnitude);

• The method of coordinates, introduced by Descartes and Fermat, which has
  changes our idea of geometry,
  established a relation between
  algebra and geometry, and laid the
  bais for the concept of space and
  basis;

• Calculus, by Leibnitz and Newton.
  Need I say more?

• The concept of probability (Fermat-Pascal), and the connection between probability and measure.