Best way to find the source of my iMac's constant crashing

Question

My iMac is crashing 1-2 times a day. The crashes are strange in that I can still move my mouse cursor, but everything on screen is frozen. They tend to happen while using Photoshop or Safari, but during menial tasks (resizing a 3MB photo or opening a new tab), and they happen in other programs as well…even just using the Finder. The crashes have happened over the last six months but only recently became for frequent – used to be a weekly occurence, now it's happening every day.
I haven't installed anything new that might be the culprit, except for GoToMyPC which I've since uninstalled. What is the best way to find out what's causing these crashes?
I've been toying with the idea of starting with a clean slate – wiping out my drive and reinstalling Mountain Lion – to get my Mac back to factory condition. What's the best way to do this? I don't want to go off of a backup because I don't want to bring over any bad processes or programs. So what's the best way to bring over all my files? Should I just copy over the particular files from the Home folder? Any chance I would be bringing over corrupted files?

Answer 1

Reinstalling Lion/Mountain Lion Without Erasing the Drive
Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.
Reinstall Lion/Mountain Lion: Select Reinstall Lion/Mountain Lion and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
To do an Erase and Install of Mountain Lion:
Install or Reinstall Lion/Mountain Lion from Scratch
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Erase the hard drive:
  1. Select Disk Utility from the main menu and click on the Continue button.
  2. After DU loads select your startup volume (usually Macintosh HD) from the
      left side list. Click on the Erase tab in the DU main window.
  3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on
        the Security button and set the Zero Data option to one-pass. Click on
      the Erase button and wait until the process has completed.
  4. Quit DU and return to the main menu.
Reinstall Lion: Select Reinstall Lion/Mountain Lion and click on the Install button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible
            because it is three times faster than wireless.