The Animation Nodes addon for Blender comes with several nodes to accomplish a wiggle effect. This tutorial explains in-depth all the options and internals.

The wiggle effect is know from After Effects and is a kind of smoth random movement. In Blender it is available as the noise modifier for f-curves. The animation nodes addon ships several nodes to wiggle numbers, vectors and even euler and quarternion rotation. Those offer a lot more control than the aforementioned noise modifier. This tutorial compares the noise modifier and it's options to the wiggle nodes in the Animation Nodes addon and explains all the settings. It is a very general tutorial and you should also watch it if you want to find out more about the wiggle function in After Effects or if you are using any other software that uses perlin noise for procedural animation.