I've designed a few items that require some form of 'Random' (search 'Electronic Dice' for a primitive example). Most applications for 'true' Random are things like Games of chance, and usually require the User to Switch-On. Nobody keeps their finger on a Button for the same length of time, and if you're simply incrementing a variable (like a Timer as Darrel suggested) until the finger is off the Button, the chance of getting the same value twice is pretty minimal. Generating Random isn't difficult, generating 'equal weighting' for something like a Dice throw is a little more tricky!

There is a place for 'Pseudo-Random' too. Especially in Science (and Mathematics), where there is a need to be able to accurately recreate an experiment (or a series of calculations) even if they contain an element of randomness.