Besiege is a physics based building game in which you construct medieval siege engines and lay waste to immense fortresses and peaceful hamlets. Build a machine which can crush windmills, wipe out battalions of brave soldiers and transport valuable resources, defending your creation against cannons, archers and whatever else the desperate enemies have at their disposal. Create a trundling behemoth, or take clumsily to the skies, and cause carnage in fully destructible environments. Ultimately, you must conquer every Kingdom by crippling their castles and killing their men and livestock, in as creative or clinical a manner as possible!

Basic Info
I don't know the best way for me to describe Besiege, it's an odd little title which is the first from Spiderling Studios. Besiege at it's core is a puzzle game as you have to try to compleate the objectives given to you, hwoever how you do that is where Besiege shines as it has an excellent physics engine and art style that makes failing just as enjoyable and succeeding.
It's currently available on Steam for 4.99 GBP or your regional equivalent (about 6-7 USD).

To be honest the best way to explain this game is to just show you. So here you go:

A Kotaku article showing off some awesome builds.

Some other cool stuff: