With the original Xbox (the one in the top pic), you couldn't fix the error where the ring would stay red and the console wouldn't respond to anything. If the hardware broke, your Xbox was screwed. XP
As for the Xbox 360, most of the time you could fix the red ring of death if you knew what to do. The error with the three flashing red lights usually meant the power supply was bad, or a part had been detached due to overheating.
What people could do was open their Xbox 360, and replace the materials that held the parts in place. The problem was that this was very hard to do, and pretty time consuming as well. Plus, it was also very dangerous. XP