There are several common ways people can verify file system integrity in OS X, including booting to Safe Mode, using Disk Utility, or running the 'fsck' tool. These options have had some people wondering which is best.
Troubleshooting Mac OS X 10.2.8: fsck issue clarification; Printer Sharing
Odds & Ends: Password length; Update utility; Using su in Terminal; FSCK at startup slowdown
Troubleshooting Mac OS X 10.2.8 (build 6R73): PCI cards; fsck; Printer Sharing; Repair Disk Permissions and black screens
The boot drive's format and partition structure can be checked both in the OS X graphical interface and in the Terminal.
The recent OS X 10.9.2 update fixes a persistent Safe Mode bug for some, but there are alternative approaches to this issue for those still affected.
While OS X includes some robust tools for troubleshooting, there are a number of third-party tools that can help tackle problems or simply give you a better understanding of how OS X functions.
Using the -n option to prevent disk corruption in Mac OS X
Apple supplies various alternate boot modes for OS X, but sometimes systems get stuck in them.
If you find a folder called Damaged Files at the root of your hard drive in OS X, it may mean nothing -- or it could be a sign that your drive is failing.