After Effects: Generate floating effects (smoke, particles, plasma, light, etc)
This effect can be achieved by using different particle systems. 



I've almost done the same thing for TV-show intro. It was done with Red Giant Trapcode Particular plugin, see the result here.

You should move your emitter in 3D space with different particle settings for different effects. Also see this tutorial on how to work with Trapcode Particular.

However Trapcode Particular is pretty expensive. After Effects is shipped with the following built-in particle system effects:


CC Particle Systems II
CC Particle World
Particle Playground


You can try to reach same result with them. But they have poor set of settings.