When I was a kid, my brother and I would play a lot of single player games together by swapping controller every time a level was completed or a life was lost. Mainly Crash Bandicoot, which was a favourite of both (his favourite was Warped and mine was Cortex Strikes Back), although we also played Spyro, Ape Escape, Abe’s Odyssey, Metal Gear Solid and the Resident Evil series this way, too (with slight variations to take into account for the longer levels).
We’d also play Crash Team Racing in competitive mode too. We didn’t have the 4-players thingy, so when friends came home, we’d swap controllers regularly. Fun was guaranteed for hours. I miss those times.