In this tutorial I take a basic look at the various random number methods in After Effects expressions. I go on to use some of these techniques to build an earthquake effect that you can easily adjust with a series of sliders. The tutorial is aimed at intermediate After Effects users who have some experience with the program and are looking to learn more about the power of expressions.
http://ae.tutsplus.com/tutorials/motion-graphics/shake-it-up-with-an-expression-earth-quake/

After Effects, my dear Watson! This tutorial uses hand drawn elements, textures, and pre-matted motion elements to recreate a look that is similar to the Sherlock Holmes credits. It gives you basics to build on. The great thing about this effect is that it is made to look organic and not 3D and effects heavy, but it still turns out looking really professional. It does not require very much expertise in free hand drawing seeing that all you have to do is trace a still image. Take this tutorial and build upon it to create something awesome.
http://ae.tutsplus.com/tutorials/motion-graphics/discover-how-to-recreate-the-sherlock-holmes-end-credits-effect/