Proportional Representation
One of the things our government is based on is the idea that you get as many congressmen (not to denigrate the fine congresswomen) as you have population. What if instead of doing this, you received a number equal to the number of votes your citizens cast in the presidential election?
This would certainly spur voter turnout as states would be desperate to protect the number of delegates they receive. It would also cause them to try anything possible to make voting easier. One nice benefit of this is that young voters would likely earn more power. They would vote in higher numbers and it would swing the power away from the older voter. It also would give greater power to those most interested in using it.
It won't happen as it would require a constitutional amendment, but the thought experiment is an interesting one to go through.