In the general (and most popular) structure of the blues, called the '12-bar blues', the dominant chords are used for the key of a particular song. So for example, in the key of E, you would use the E7, A7, and B7 chords for that structure.
In some cases however, and when you need an extra 'modal' sound or "less happy" tonality, you would instead use the minor chord. So instead of E7, you would play Em. This results in a completely different sound in a blues structure. Many bluesmen and jazz players used their own variations on the common 12-bar blues to add some variety. These added chords or the mellow minor sound tend to shift the blues sound to R&B or soul territory, as well as more variety in soloing to use more extended scales and chords.
The most popular minor blues song is by far B.B. King's 'The Thrill is Gone':
Some other great minor blues are:
'I Hear Nothing But The Blues' - Albert King
'Midnight Blues' - Gary Moore
'Double Trouble' - Otis Rush
'Moon Blues' - Otis Spann
'Who's Been Talkin' - Howlin Wolf