adb doesn't recognize my Nexus 10 on Windows 7. Here's what I've done:
I had the same problem on Windows 7.
First make sure the Nexus 10 developer mode and USB debugging is on ( if you dont see developer options, tap on About Settings -> Tablet -> Build Number a several time and it should activate developer mode)
Check if your ADB driver is in good shape by going into the Device Manager. If not un-install the ADB device manager and re-install it by pointing Windows to Android SDK location (It should pick up the driver automatically).
Once it is installed and still it does not work. Go into Settings-> Storage -> USB Computer Connection and select PTP option. Reconnect tablet to the USB.
Hope it helps!.