I have a bunch of wall warts of widely varying DC output voltages. I find that they almost invariably show a no-load (or low-load) DC voltage considerably higher than their stated rating. I'm wondering about what physics is causing that. I assume that a load much closer to their rated max current will bring the voltage much closer to the rated voltage. I guess the moral of this question is "Always use a voltage regulator capable of encompassing the no-load condition". Any tips on their use that will not damage the electronics they're intended to drive? Thanks.
The answer to your last question is that you can use them on the electronics they are designed to work with, since the designer took into account the unregulated nature of that kind of AC adapter (quickly becoming an endangered species, by the way, as regulated types take over).
An unregulated adapter is typically nothing more than a transformer, a bridge rectifier and an electrolytic capacitor. The average voltage drops as ripple increases, plus the transformer has some output impedance and the diodes drop more voltage as current goes up. So the average output voltage decreases and output ripple increases the higher the load current is. Typically the output voltage is specified at the maximum load.
The more common type nowadays is the regulated switching adapter which are typically much smaller and lighter for the same amount of output power. They do drop in voltage slightly from no-load to full-load, but it's typically a small amount (like maybe <2%).
Some may be regulated.
There are designs of regulated supply that lose regulation at 0 current, needing (for example) 5 mA load to maintain regulation.
So, re-test with 1 kilohm load and see what difference that makes.
If it's much closer to rated voltage, increase the load (meaning reduce the resistor) a bit more. If it barely makes a difference, that's an unregulated supply.