I have a Nexus 4 with Android 4.3 and I am trying to connect the device to a computer with Windows 7 64bit.
I installed the latest drivers and the latest adb>
Сhange USB connection mode from MTP to Camera (for Nexus 7) or, possibly, to Mass Storage or something else (for other devices). This option is usually under Settings -> Storage. Then connect the device again, you'll get the authorization dialog.
MTP has been known to interfere with USB debugging -- these two did not work together at all on majority of older devices. Nexus 7 and many newer devices do allow both to work alongside, but this particular issue suggests it's not all that smooth yet.
Bonus -- checklist for when adb is not behaving well:
adb kill-server followed by adb start-serverSettings -> Developer Options -> USB Debugging -- switch off and on/etc/udev/rules.d/51-android.rules (again, universal solution: https://github.com/snowdream/51-android)~/.android is owned by you, not root (and upvote this answer)