0.1 uF caps next to ICs

I know it's good practice to do this to filter out noise from the power supply. What about your regular old 16x2 LCD displays? Is it good practice to use one close to their Vcc & Vss lines? Or do they already have one built in all that little chip on the back of them?

I think it's good practice. It's probably not necessary (as there should be some built-in to the module), but adding caps at the power entry to modules just gives me a warm fuzzy feeling that it's more likely to work and helps create a cleaner overall power distribution network. Given how cheap caps are, it's a cheap way to feel warm and fuzzy. In fact, they may do as well preventing noise from going FROM the LCD TO the rest of your circuit as the other way.

I worked with a graphic LCD once that absolutely needed a cap on its RESET pin, otherwise the noise coming FROM this pin was sometimes enough to cause the LCD to spuriously reset itself! That was truly weird.

So...caps are good...use them.

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...I had a warm fuzzy feeling that this was the case! Never thought about noise coming FROM the LCD, but good point.
thanks.

Since its a circuit board they are trying to sell they will have put decoupling on it so it actually works reliably.

Decoupling caps aren't best though of as filtering out noise, their job is to keep the supply near the chip pretty constant despite high speed current noise (switching transients) that would otherwise induce large voltages along the supply traces on the PCB due to stray inductance. On a large board without decoupling you would expect the supply rail entering a digital logic chip to have several volts of switching transients and to misbehave.

The decoupling capacitors prevent this and turn the rapid current spikes into much gentler current noise at lower frequencies, eventually the regulator does the work once this is low enough in frequency. Often there will be a 22uF or similar capacitor to push the noise lower in frequency than the 0.1uF can manage (this doesn't have to be so close to the chips though).

No, the noise is nothing to do with the power supply, that's a confusion with a smoothing capacitor I think.