The original front-loading NES is quite infamous for having a poorly designed cartridge mechanism that bends and loses contact with the game cart pins. This is why people were always blowing on games and jamming them back in the NES back in the day. The later top-loading NES fixed the problem but is kinda rare and doesn't have RCA video outputs.

I don't think the original Xbox had many reliability problems though, maybe you're thinking of the Xbox 360 and its red ring of death problem?