FireWire Disk Mode
One Mac hardware feature which is especially adored by Mac geeks is the ability to access the internal hard drive(s) directly, bypassing the operating system. The Mac becomes an expensive enclosure. This means that when you need to run diagnostics on a drive, you don't need to pull it out. All you need to do is hold down "T" while you turn the Mac on, until you see a FireWire icon on the screen. (If you see a grey Apple, power off the Mac and try again). Then, attach a FireWire cable from the user's Mac to your own and the user's drive becomes available to you on your own computer (very useful, for example, for running either of the previously-mentioned tools).
It's also handy in the other direction: you can put your own Mac into FireWire Disk Mode and start up the user's Mac with it-which can help determine whether a problem is related to software or hardware. To choose which drive you start up from, hold down "Option" as you turn on the Mac until you get to the graphical boot chooser. Again, if you see a grey Apple, power off and try again. Two recent laptop models lack a FireWire port, so you can't use FireWire Disk Mode with those. You'll need to start them from a USB external drive or pull out the internal drive.
Want to see what kind of RAM is in which slots? Not clear if a USB device is being recognized? System Profiler is your friend, giving you a window into much of what's under the hood of a Mac. It's part of Mac OS X in the Utilities folder of the Applications folder, or you can simply choose Apple Menu->About This Mac->More Info.
ID-Design's WhatSize is the program you want when your user's drive is full but he or she can't figure out why. It will allow you to very quickly drill down into the heaviest folders and files with a highly intuitive interface. Be sure to run it in Administrator mode, as this will allow it to see inside folders belonging to other users on that machine-which is often where large, abandoned files such as iTunes libraries lurk. WhatSize once helped me figure out where a misbehaving printer driver was spooling endless temporary files, filling the disk.