I've been placing capacitors around linear regulators almost out of habit for years now. I remember the typical old "recommended circuit" in the datasheets, and I add to that what I occasionally read about stabilizing the output voltage and preventing spikes/dips. The result is that now my starting point for a design with 2 regulated voltages looks like the attached circuit. That's 2 ICs, 7 ceramic caps, 3 electrolytic caps, and 2 diodes, and I haven't even placed my first component.
From what I've googled, the questions regarding this topic are usually "how safe can I make it?", rather than "how many components do I actually need?".
From observation and going over a lot of circuits:
The minimum starting point with the LM78xx chips seems to be a 1uF cap on the input and 0.1uF cap on the output. When I look at real-world implementations, however, I'll often see one of each (1uF and 0.1uF) on both sides. Most LDOs that I've looked at don't need the 0.1uF on either side, but rather require larger, ~10uF caps (depending on the load) on both sides.
With any voltage regulator, you'll see a reservoir cap (electrolytic/tantalum) on the output if the load could ever go over ~50mA. If the input current is coming from anything but a battery which is located within an inch of the circuit, the input will also have a reservoir cap.
If there's any chance at all that the input could go lower than the output (primarily if the input is shorted for some reason, but also because of larger reservoir caps on the output) a protection diode will usually be present.
Taking the above into account, it seems that the attached circuit is a reasonable starting point, despite the fact that its component count could be higher than the rest of the circuit.
I know that the characteristics of the circuit will effect the necessary capacitors around the regulators, but I'm looking for some rules of thumb. How many of the caps can I "safely" omit?