sometimes more than 100nF are required, for instance if you drive LED displays.
1uF, 47uF or even 220uF, if problems persist, add capacitors at multiple places until they disappear.
fast computer circuits (let say, 10MHz), which have RAMs, GALs, etc.,
need 100nF, 220nF or 330nF everywhere, not just one or two.
a CPU will introduce current surges in the 10s and 100s of mA, and if there are no capacitors, it can and will introduce logic glitches, means, the design can not work correctly.
for low-power PICs including some LEDs, i often just use 1 uF (note i supply via USB or battery, if you have 7805 etc., situation is completely different).