Here's a nice little introduction I found with some reductions on the first couple slides: http://www.cs.princeton.edu/courses/archive/spr04/cos226/lec...

I just finished my algorithms undergrad class last semester; one of the questions on the final was 'you are a terrorist looking to cut off supplies to your enemy, which 3 nodes must you destroy to cut off the supply network?' And there was a complicated graph with probably 10 nodes and twice as many edges (very difficult to brute force in the allotted time), and we had to find the min-cut which would severe the flow. Some really cool problems reduce to max-flow.