I regularly ran XP for a week at a time, perhaps several weeks. Usually updates would come in by then, necessitating a reboot.
Throughout the history of Windows, stability has largely been a matter of two things: shitty hardware (with equally shitty drivers), and shitty programs.
Back in my Win98SE days, I seem to recall the most frequent offender was Acrobat Reader 6. If I was reading a lot of datasheets, I might need to reboot twice in one day! Most days, I shut down for the night anyway, which was fine as it started up fairly quickly (being on rather new hardware by then, compared to the OS). I don't remember if I ever went more than a week without a reboot.
I have a stock IBM Pentium with Win95 on it, of course I barely use it, and not for many diverse programs, but I can't seem to attribute any problems to the hardware or drivers, that's not due to simple bitrot (a lot of programs do happen to be suffering from file system errors..).
I've never had a problem with leaving WinXP or 7 running for weeks on end, with the random reset almost always being the fault of updates, bad programs (e.g., a game that captures the display, crashes, and the desktop doesn't return), or power failures.
I'm not saying everyone should have this experience, because obviously, most haven't; but I want to remind those that haven't, that their cases are exceptional, and stable operation, with a good combination of hardware and drivers and programs, is perfectly possible.
And by the way, all those billboards that BSoD'd? Process those through this filter for a moment. What do they have in common? Custom display hardware. What else do most companies have in common? Bad drivers. So, it should figure that the most [publicly] visible displays are also the least stable!
Tim