Liquid armor is here
Researchers at University of Delaware have developed a form of liquid armor which can protect the entire body as opposed to just the chest like current kevlar vests. The liquid - called shear thickening fluid is actually a mixture of hard nanoparticles and nonevaporating liquid. It flows normally under low-energy conditions, but when agitated or hit with an impact it stiffens and behaves like a solid. This temporary stiffening occurs less than a millisecond after impact, and is caused by the nanoparticles forming tiny clusters inside the fluid.
You can check out some pictures and video of the armor here. It's a good idea, but who knows how effective it'll be under actual circumstances. The video has an example of the armor under testing and - although the bullet doesn't puncture it - if there was a person behind there they'd be in serious need of medical attention.