Both Chris and Vertigo are right...
The main thing that makes the blues is putting a b3 over a natural 3. Try it out - in the key of G, play the major third note (B) and the minor third note (Bb) together. That's done easiest by playing 3rd fret G string and the B string open. Nasty, right?
The second thing is the "blue" note, the b5 (Db). A.k.a. the tritone interval (6 frets, from G to Db), this combo sounds pretty bad too... Try hitting 2nd fret B string and 3 fret high-e string. These intervals (minor second, diminished fifth) are the "worst" sounding of all thirteen (unison to octave) in western music. In fact, the tritone was known as tthe "Devil's Interval" back in medieval times.
These intervals were chosen to simulate the underlying pain/anguish theme of the blues. After years of usage, these intervals became less and less "out-of-place" and now it's common to use them (the blues scale is one of the most common scales used in rock music, and the first scale learned by many). Just goes to show you how music evolves...