Originally Posted by ElephantSack

Rage Against the Machine is an obvious top choice.

And thank you for not posting this in the Punk category. Although people tend to exemplify punk rock as the most rebellious or socially-aware music around.

Usually, one of the things I look for in a band is poignancy. So here's some of my tops that at least have select moments of political/social intensity.

Immortal Technique
Soundgarden
The Who
The Clash
NOFX
Bad Religion
Tom Waits
The Roots
Les Claypool
Pink Floyd
Tool
Corrosion of Conformity