Honestly, it's not something I've actually run into- there's only been a handful of times I can think of where a system's broken down or a game's acted up during play- and usually, it's either early in play or it's running well enough to get to a save point. Then I can turn it off, clean the game/console, and start again without issues.
Right now I have 2 systems that are kinda-sorta out of comission. My 7800 needs a color adjustment- it's displaying very green right now. My Channel F's button 2 has quit working. It's sad when a machine breaks down- I tend to get attached, and it can be difficult to find someone to do repair work. Despire that, I know getting a replacement console is always an option, so I don't worry too much.