My cheapest fare was about ten years ago in the dying days of Eastern right after the last strike when they were offering one way fares on the Shuttle for $12. We grabbed that DCA-LGA one evening coming back from work in Northern VA despite the fact that our car was parked at EWR. Even with the cab fare to get the car the next morning on the way to work, it was a real bargain. As a bonus, they did not even have the regular Shuttle equipment on that flight and the regularly configured plane allowed the first passengers on board to sit in First Class.
Therefore, we ended up getting FC tix DCA-LGA for $12.