The best thing that I can remember making with K'NEX was a ferris wheel, and I followed a set of directions. However, a couple of engineering-crazed kids from Olin College have devised a gigantic K'NEX Binary calculator that can add or subtract numbers as high as 15 (That's way more impressive than it sounds).
It works by utilizing 9 little balls that you drop down from the top, think Plinko on the Price is Right. As they fall certain levers are flipped that in turn move a flag that shows you what number is being entered. The first four balls (remember they're using binary) tell the machine what the first number is, the fifth ball says whether you're adding or subtracting, and the last four indicate the other number.
Here's a very confusing video of the calculator in motion. I will never under-appreciate the free little calculators that my bank sends me ever again.