Major disk manufacturers have usually provided their own diagnostic/repair tools. These run from Windows and/or a bootable CD and allow extensive surface testing, low-level formatting, and defective sector remapping.  These tools don't generally care what kind of file system your disk contains, being concerned more about it's raw storage abilities.

When using a Windows operating system however, there are are a range of other issues that may arise - including accidental file deletion, junk file accumulation, and inefficient file storage (fragmentation).  To deal with these, some of the most useful, well-designed, and professional-grade tools are by a company call “Piriform”. While all of their products can be reached from their home page, I've included more direct links with each description.

SeaTools	Seagate's tool will work best with their own drives and those from Samsung, LaCie, and Maxtor (product lines acquired by Seagate)	Ignore the Windows version unless you have a dedicated workstation for testing multiple (secondary) drives.
Data Lifeguard	Western Digital's tool may work with Hitachi drives (acquired by WD) but the old Hitachi "Drive Fitness Test" is still available here.	Since only a Windows version is available, apparently you first need a working, bootable (Windows) drive in your PC to diagnose/repair a failing or non-bootable drive.

Recuva	If you have second thoughts about a file you just deleted - or even one you deleted last week - this might be able to get it back (or at least part of it).	It will also give you some idea why you should use something like DBAN before giving away your old PC.  Note: If you have VSS taking periodic snapshots, ShadowExplorer may be an even quicker way to recover deleted files.
CCleaner	Cleans up temp files, caches, browser histories, and other files that waste disk space and potentially compromise your privacy.	Originally called “Crap Cleaner”. Also does registry and restore point cleanup.  Of course, be careful you don't "clean up" things you are using - like your web password cache.
Defraggler	Defragments both files and/or free space to reduce excessive file access times caused by drive head "thrashing".	Oddly enough, even if your disk is half empty, files can still get fragmented. Note: Defragmentation is nearly worthless for a modern SSD used by Windows 7 or later - it could actually wear out the SSD faster.