Counter anecdote mode: engage!
As an owner of many Nvidia cards, I find they crash infrequently, and when they do it's because:
* I was running Windows 8 Preview and pre-release Nvidia drivers
* There was some sort of hardware problem with my systems
I have used four ATI/AMD graphics cards over the years. Not all of them were negative experiences, but none of them were relatively more positive than using Nvidia hardware.
Before that, I had an ATI HD 5870 for over a year. I had about 3 crashes on the desktop, some that lost me work. The anger from losing work is what I remember most strongly, and made me vow not to buy ATI next time.
Before that, an 8800 GTX. I had 0 crashes from the desktop over several years.
I was running Nouveau drivers on the 670 for no more than 60 seconds before it crashed.