Mountain Lion on Unibody late-2008 Macbook? I'm currently having a late-2008 Unibody Macbook with Snow Leopard installed. It runs really great!

However, I'm thinking of installing Mountain Lion. Mainly to use Filevault 2.

Will my Macbook run with ML?

It has the following specs:

2 GHz Intel Core 2 Duo 
4GB 1066 MHz DDR3 
40GB Intel 320 SSD
Your system specs are above the minimum requirements, so you should be fine. Lion and Mountain Lion do require more than the 2 GB RAM than Snow Leopard needs to run smoothly, in my experience. You've already got 4 GB, so that should be okay for all but the most busy systems with many large apps running simultaneously.