Softie Collision System
aflatsprite
Does it require meshes to be manifold?
No, it automatically uses a different algorthm for non-manifold meshes. But manifold is strongly preffered.
Will this work on complex character rigs?
It can, but a much better way is to create proxies. For example if a hand is grabbing something - create collision spheres for the fingers.
You can try to use advanced mode to select phalanxes of the figers by using vertex paint.