What should you do if your OS X system fails to boot, being stuck at gray screen with the moving wheel? What to do if your OS X system fails to boot, being stuck at gray screen with the moving-wheel?

The system boots from recovery partition, it does check the partition but it will not boot.
The OS X boot process is chock full of little tasks in parallel and sequence, but it boils down to three major parts:


Gray Screen - Hardware governed / POST / EFI / locating a boot image.
Apple Logo on Gray Screen - System level OS X processes start.
Blue Screen - User level processes starting.


Since you haven't gotten to the blue screen - it's not anything in your user account as the system itself hasn't booted. Rather than guess what exactly has caused it, I'll link to the two articles that Apple has on getting to the nub of startup issues.


If you see a gray screen at startup 
If you see a blue screen at startup


I am including both since you may have to solve user issues if the cause of your boot is hard drive corruption or major hardware issues. Hopefully it's just one thing in the system startup.

If you don't have time - start with a Safe Boot (hold shift key down) to see if you need to get your recovery disk or another bootable system. If you have a backup - you can jump to re-installing the system since that should re-write everything needed to get to a blue screen. Do run a safe boot before or after to rule out incompatible non-essential system level startup tasks - it could be as simple as one launchd problem during the system start process. The system logs will likely point you to what is going on when it pauses.

Good Luck and let us know what you find out!