Hardware diagnostics would probably be the most important tool in any computer technician's toolbox, and all-in-one boot discs exist to fulfill this role. I'm partial to free, open source and simple-to-use tools hence I prefer Ultimate Boot CD for this purpose. It's not the best out there but it fits my requirements best.
Burn-in tools – CPU burn-in tools come in handy for testing for overheating issues. I don't have a particular interest in overclocking but I think overclockers would appreciate burn-in tools for testing overheating and stability of their overclocked setups.
Hard disk info and diagnostics – The most common problem I encounter would be hard disk failures. Hence Ultimate Boot CD's plethora of hard disk diagnostic software tends to be the most used for me. The diagnostic software for just about every brand out there is available and generic solutions are available for those that aren't.
Data recovery tools – Testdisk and PhotoRec are popular data recovery tools. These come in handy for data recovery attempts though I haven't had too many chances to test them out. Most hard disk failures are either minor enough for successful cloning, or too sever that nothing could be saved at all. Still, it's a good idea to have these around just in case the chance does arise.
Disk cloning tools – Personally I prefer to make use of gddrescue for cloning tasks but that's just me. If you prefer a minimal toolbox, then there's hard disk cloning tools available already so no need to look further than here.
These are just a few utilities that are available on Ultimate Boot CD. Another very useful tool would be memtest+ though I usually use the one that comes with Ubuntu. It's the same anyway so use whichever you prefer. There's lots more tools in Ultimate Boot CD, enough to cover quite a variety of diagnostic scenarios but I'll not cover them here. I don't use every tool in there so I feel it's not my place to comment too much on them.
Technician's toolbox - malicious software removal tools
Technician's toolbox - system maintenance tools
Technician's toolbox - backup tools