I own a D70, D80 and recently purchased a D7000. I have under 1K on the shutter, and have had no issues. The D7000 had some issues with some stuck green and red pixels, but this was solved shortly afterwards (was the cause for the D7000 being back ordered until recently).
The kind of widespread acceptance this camera received can indicate why there are some people having issues. This can be due to everything from the user's inability to use the camera correctly all the way to an actual hardware problem. Needless to say, the camera comes with a 1 year warranty - and if there is a problem surely Nikon is fixing it for free under the terms of the warranty. I have not had any problems with my D7000.
If you're like me - purchase an extended warranty from
SquareTrade (there are other similar providers, too). I opted for 3 years of coverage and coverage from accidental damage from handling (falling, submersion, etc.) for about $210.
I hope this helps and good luck. Please rate my reply. Thank you.