How to reinstall/repair OS X without losing files?

macos

I bought a Macbook Pro in 2012, it came with OS X Lion. (came with NO disc, etc)
1 Month ago I downloaded the update "Mountain Lion". About 2 weeks ago I removed some of the OS X Mountain Lion System files (Twitter, Facebook, etc)

After I deleted some of the system files, if I quit Notes, Contacts and other apps they freeze. I have also noticed other issues with the Mac. I have restarted, cleaned, repaired permissions, made a new account, etc but no good.

Am I able to somehow reset/repair everything, like doing a reinstall of Mountain Lion, without losing my files, apps, etc? I have no problem with the settings being set to default (I would like that).

For example, with Windows you can do a reinstall but all the files and apps are kept in a Windows.old file, and with Windows 8 you can do a config/system settings reset but all your files will be kept.

Time Machine has been disabled since I got this Mac.

Solution 1:

You can do an Archive & Install which will reinstall OS X but keep your files.
Don't forget to make a backup before you reinstall in case something goes wrong.