Integrating multiple sensors onto one board, how many decoupling capacitors do I need?
PCB traces have parasitic inductance and resistance, that is why we place capacitors close to the load. When the a load suddenly switches, the voltage drops at the load (op amps, microprocessors, comparators, sensors, ect). When the voltage drops at the load, it can lead to noise in analog systems and errors in digital system. Most circuits are built to function at a steady voltage level.

The PCB trace inductance and resistance prevents the voltage from being regulated immediately by a power supply. Power filter caps fix these problems.

You can use one power filter capacitor for multiple chips. However, there are downsides to this. 

Capacitors have ESR and ESL, which means they have parasitic effects that affect mostly the high frequency impedance of the capacitor and its ability to 'short' high frequencies (to ground). 

1) The further you place a capacitor away from a chip, the longer you have to run a PCB trace to the capacitor thus increasing it's ESR and ESL. (that means you have a possibility for more noise) 

2) A shared capacitor could increase noise, if one load temporarily dips the other load will also see it, I've shown this in the diagram below (I did not include capacitor parasitics)







simulate this circuit &ndash; Schematic created using CircuitLab

There have been times when I've used capacitors with multiple loads because space was more of a consideration, the loads were analog and were also mostly constant loads.