When it comes to troubleshooting the Macintosh, there are many utilities available for getting the job done. Some are cheap and some expensive but for most you will have to shell out a bit of cash for a license. However, there are also some very robust free options out there for troubleshooting software problems to managing hardware issues.
Even though they are free, many freeware options can be just as good if not better than the paid alternatives. While they are not necessarily pretty applications, many are simple and straightforward approaches to tackling individual problems in the system. A classic example is a very old utility, "Xeyes," that while being practically useless and not very pretty, did allow for you to locate a hidden or hard-to-find cursor in the X window environment.
Not all freeware is as simple and basic (or quite as useless) as Xeyes, and many options instead are quite useful for Macs. Here is a list of some I have found to be particularly handy, many of which I commonly recommend people use for troubleshooting problems on their Macs (click the application title for a link to the program's Web page).
AppleJack has just been updated to be compatible with Snow Leopard and has been a very useful utility for clearing caches, repairing drives, and performing a number of maintenance tasks on the system. The benefit of it is that it runs when booted into single-user mode so it can have as much access to the system's resources as possible for running its maintenance tasks.
A full-system fix is as easy as booting with Command-S held down, and then typing "applejack" at the command prompt, followed by a couple of selections from the onscreen menu, and the program will run and optionally reboot automatically.
This utility is another useful one, which can turn practically any external media into a diagnostics boot drive. If you have an old iPod sitting around, you can install a bootable version of OS X to it along with your desired utilities, and then keep the drive updated with the latest versions of each utility. Granted there are other ways to do this, but it's free and can also manage specialized bootable media such as drive repair discs.
Onyx and Maintenance are robust and well-established OS cleaning and maintaining utilities that run a variety of scripts and functions for removing temporary items, managing permissions, and turning over system logs.
If you are unsure what files and folders are using the most space on your hard drive, Grand Perspective will display them in a grid of squares whose size represents the relative amount of disk space being used. If you open the program with proper read access, it can be used to size up system files as well, including caches, logs, and other hidden files that may take up a fair amount of space over time.
In addition to viewing files in the program, you can use the program to directly delete specified files, though this feature is turned off by default.
Along with Apple's supplied disk utility is the command-line "diskutil" program, which can perform similar fixing routines in the Terminal (either when logged in or when in single-user mode). TestDisk is another command-line tool for disk repair, but it's far more robust and allows you to recover lost partitions, undelete files, and manage and fix boot sectors for a variety of formats and partition tables, including FAT, HFS+, NTFS, ext2/3, Novell, UFS, JFS...the list goes on.
The utility does take a little getting used to and will require a small amount of terminal and Unix familiarity; however, it can be exceptionally useful for fixing damaged drives.
This is another maintenance utility that, like OnyX and Maintenance, is completely free. It runs periodic maintenance tasks, but in addition has a number of system-tweaking features (showing hidden files, forcing trash to empty, relaunching the Dock and Finder, etc) that can be useful for getting around odd hangs and slowdowns and other odd system behavior.
If you use Boot Camp or external drives that are formatted to NTFS, you may find Apple's built-in support for NTFS to be rather limited (you can only read the drives). NTFS-3G is an open-source file-system driver that will allow you to take advantage of many aspects of the NTFS file system beyond just reading and writing.
Hardware diagnostics is crucial, and Apple includes MicroMat's TechTool Pro with the AppleCare DVD so you can test your hardware for problems if your computer is not working properly. RAM problems can be a common area for system failures and can go unnoticed if the bad areas of RAM are not used frequently, so running a testing utility to read and write data patterns to as much RAM as possible will ensure the RAM is working fine. Rember is a GUI front-end for the open-source "memtest" utility and will ensure your RAM is working as it should.
The system may slow down if components get too hot and may crash if there are no safeguards against overheating. Overheating can also greatly reduce the lifespan of the system, so being able to read the internal sensors for components' temperatures is exceptionally useful. Many components such as hard drives, CPUs, other controllers, chassis, and GPUs all have temperature sensors in them, and graphing the temperatures when performing certain tasks can help show when the tasks are completed.
If you are an IT professional or have advanced knowledge of how networks function, Cocoa Packet Analyzer may be exceptionally useful to you. This utility will capture and analyze packet trace files and show details of TCP dumps so you can optimize your network setup and diagnose problems. It is definitely targeted for people who know a thing or two about networking and can be used along with a number of Apple's included Unix commands for analyzing network problems.
Do you have any additions to this list? If so then post them in the comments below. Keep in mind we're looking for freeware options (donationware is acceptable as well) that can help Mac users troubleshoot and fix problems on their Macs.