Most of these answers seem to be defining the blues by the type and quality of emotion it conveys. However, I have to agree with McGrath, that these emotions are more universal than that, and appear in musics of all kinds that otherwise have nothing to do with the blues. To be meaningful, I think you need to define the blues historically and musically, rather than just emotionally. The historical part of the definition involves where the music came from -- black slaves, ex-slaves and descendants of slaves combining African elements from their cultural past with the musics they encountered and assimilated after their arrival in America. A lot has been written about this, and rightly so -- the "roots of blues" is a fascinating topic for the musicologists among us.

For me, the musical part hinges on the amibiguity of the third step of the scale -- where other western musics had increasingly moved in the direction of a definitive major or minor tonality (pick one -- can't have both), the blues mixed major elements with minor, playing a flatted third against a major chord progression, etc. This is more significant than it sounds, because it very effectively conveys a complexity of emotion that often is not present in other musics that are based on a more definitive major/minor choice. Where a simplistic view would consider major scales/chords to be "happy" and minor to be "sad," the mixing of the two allows both emotions to be present in varying degrees -- which allows joy to triumph over anguish, or sadness to exist in the midst of happy circumstances, etc. I believe that this is the essence of the blues, and some of us might argue that it more truly reflects "real life" than the more stark choice offered by defined major and minor tonalities in some other musics.

I may not have expressed this very well, but I hope it makes sense to other Mudcatters. I'd be interested in people's reactions.