My Mac Pro's PCIe SSD actually became unrecoverably corrupted a few days ago and I just went through what you're experiencing.
Option 1 Recovery Mode: boots from the special recovery partition that is established when OS X Mavericks is installed. You can perform basic system diagnostic and fix tasks, such as
Disk Utility.app (Repair Disk, Repair Permissions, etc),
Terminal.app (more advanced debugging), etc. Try Repair Disk and Repair permissions here before trying Option 2.
Option 2 Reinstall OS X: As long as you don't decide to wipe the hard disk via
Disk Utility.app Erase or Partition completely, your data will be mostly preserved. To my knowledge, reinstalling OS X overwrites essential directories used by OS X, including:
but leaves the following alone:
My Advice: Try Option 2 first. Then, if that fails and you possess a Time Machine backup, wipe your hard disk completely via
Disk Utility.app's Erase tool, reinstall OS X clean, and then restore from a Time Machine backup or copy files from your Time Machine backup piecemeal.
Hard disk corruption is a nebulous thing. You don't know what blocks are suspect. Completely reformatting to a fresh HFS+ partition is the "cleanest* approach, as long as you can preserve your data.
How to create a clean Mavericks install USB key: http://osxdaily.com/2013/10/23/create-os-x-mavericks-install-drive/