Some components can be taken apart to salvage pieces of them which are still usable even if the whole isn't.
The magnets in unusable hard drives tend to be quite powerful and can be taken out. This can be a bit of a rough process. At least one Torx screw needs to be removed for this. Also, if the logic board on a hard drive is broken, another one from the exact same type of drive can be used to replace it.
The laser in a CD or DVD drive can be removed. Lasers from DVD writers can be used in laser engraving devices.
Aside from the relatively common DIMMs or SODIMMs, may contain CF cards and oddball CPUs.
Do *not* attempt to do disassemble CRT monitors. Like power supplies, they contain large capacitors which can deliver a very nasty jolt, but the capacitors in monitors operate at even higher extreme voltages and can be far more dangerous that those in devices like power supplies.
CRT screens are in general quite dangerous devices. It is necessary to be very careful and make sure they do not fall, aside from being very heavy they can release toxic chemicals if ruptured.
The stands for some flat panel displays are detachable and standardized, hence they can be swapped between one monitor and another. This is especially useful if an extra stand is more adjustable, particularly if it pivots.
Many LCD screens also have external power supplies, and as a result their effective power consumption can be affected by whether they are using a more or less efficient power supply, and this can be tested. Naturally this can also be true for other devices that use exchangeable power supplies.
The mounting brackets on motherboards appear to get damaged somewhat commonly, making them likely to be worth removing and saving in case a replacement is needed.
Some motherboards have copper heatsinks. These are more effective and expensive than basic aluminum versions, however, this is not because of copper being worth greatly more, it is mostly because it's harder to machine than aluminum.