Soon after launch, the Xbox 360's hardware issues became infamous on the internet. The so-called "Red Ring of Death" problem plagued the early Xbox 360 models for years, and Microsoft offered little initial support for fixing them. Three flashing red lights around the Xbox 360 power button instead of the one to four green lights indicating normal operation represent an internal problem that required service.
In 2009, after multiple minor hardware revisions intended to fix the problem, Microsoft finally extended the warranty of the Xbox 360 to one year, allowing most people to return Red Ringed consoles if the problem arose. This allowed Microsoft to exchange the consoles sent in for more modern SKUs, which had shifted the chips and shrunk them to remove the root overheating problem.
More recent Xbox 360 models have not had the Red Ring of Death issue in any significant numbers, and it doesn't appear to be present in the Xbox 360 Slim at all.