I played through Final Fight on Capcom Collection for Xbox. You essentially have unlimited health because when you die you can just "insert coin" and continue to play horribly and never have to start over.

And unfortunately I don't have a Final Fight machine set up in my living room to able to experience this game the way it was meant to be played- fighting transsexuals and dumping boatloads of quarters from your dad's vintage coin collection into the machine.

What are some other games like this that because of the limitations of console games, you essentially have a handicap that can't be removed?