I've seen posts here that talk about the low component count of the MAX7219 only needing 2 capacitors, and I've always used it with a 0.1uF cap across the power supply, so I wondered why they said it needs 2. I finally looked at the schematic that keeps getting linked and it has a 10uF and 0.1uF cap in parallel across the power supply.
What is the purpose of doing it that way? I understand that the 0.1uF is intended to smooth short, sharp voltage spikes and using a 10uF is intended to smooth out ripples over the longer term, but won't the 10uF also deal with the spikes if used alone? It's not like the 0.1uF will act faster or anything.
In theory any cap bypass cap has less and less capacitance reactance (AC resistance) to ground (which is good , acts like a high pass filter to ground) as the frequency of the noise or spike increases. However in practice different capacitor's dialectic material used for a specific kind of cap can have different ESR (equivalent series resistance) values at same frequencies. So larger electrolytic caps are favored for their effectiveness at lower frequencies (for say AC power ripple frequencies) while ceramic caps are better at higher frequencies. Also where the caps are placed can have a big effect on how well bypass filtering work. The larger caps work better by placement at where power enters the board or right at the output of a voltage regulators, where as the smaller popular .1ufd caps are usually more effective mounted right at the Vcc terminals of any ICs being protected. You will note that the arduino board design for a 328p chip has 3 .1ufd caps wired close to the chip at the Vcc, Avcc, and Aref pins, all used for bypass filtering.
That leads to what do words like required, needed, recommended and such mean when designing ones own circuits. A lot is gained from past experience. Also checking the datasheets for any ICs being used and be useful, some ICs are assuming and require such external bypass filtering, while other chips are less sensitive to the typical noise levels. I usually when designing a circuit used the minimum number of filter caps I thought I could get by with, however I also used at least one .1ufd ceramic cap mounted right at the Vcc pin of any IC used in the circuit. I typically had less problems following that rule. However there is no perfect rules that will always solve and prevent noise caused problems, following good general practices is just the starting point and further debugging may always be required in some cases. A good O-scope is very useful for problem circuits you are first building. But so far I've found simple AVR 328p circuits to be pretty trouble free using just typical bypassing rules.
Others may have better or further recommendations based on their specific experiences.