As people seem to be agreeing, the plug and play cables of consumer electronics are going to tend to be somewhat protected from common scenarios, in various ways. For the most part (due to static and EMI consideration as well), they are not going to connect a microcontroller pin directly to some jack on the exterior of the device; if they do, it will be specially designed for that.
This situation arose when connecting one naked microcontroller output to to the input of another microcontroller (no special protection except what is built into the chip), with separate power supplies such they won't both be turned on or off at the same millisecond. Since I was connecting both ways (master out to slave in and slave out to master in), there was not way I could power down both at the exactly the same time.
Basically, such situations can and often will occur any time you are jumpering microcontroller based electronics together in some circuit with more than one power supply. So if your Arduino is powered by USB but connected to a breadboard circuit with its own power supply (say a sensor or actuator of some sort), can you turn the two supplies on and off at exactly the same time? What if one side is battery powered?
One concern is damaging a microcontroller. My suspicion is that while it's not a good idea, it probably isn't super sensitive to this because most people who have ever used two power supplies while prototyping have probably run into it without noticing. Using a resistor between the microcontroller might help some.
If one accepts Grumpy_Mike's model that an unconnected VCC in the slave is effectively at 0V, then no input to an unpowered microcontroller should ever be above 0.5v, period. In addition to two processor situatins, think of something like in analog input connected via voltage divider to a battery or solar panel, used for voltage monitoring when operating normally. I suspect we have a bit more slack than that model (and that there is a difference between leaving the VCC input unpowered and actually tying it to ground), but you can decide for yourself and caution is wise. I would certainly not advise deliberately using phantom power, but I'm not going to say "never, ever use two power supplies that cannot be powered or unpowered within milliseconds of each other".
Total current is another aspect. In my case, the slave ATmega328P was powering itself, two small on-board LEDs, and the output that returned to the master. If it was in a circuit to put out 40ma on several pins, obviously it would have attempted to draw more current from the 40ma output of the Master (from which it was drawing phantom power). Maybe that would have been more problem for the protection diodes, or even the Master's output. So the more power your controller might draw via an input, the more you might want to be concerned.
(Since I'm using DIP based Arduinos, I may order another ATMega328P from Mouser for $2.50 next time I have an order, and keep a spare around).
The new caution I learned was that we should be aware that the "unpowered" microcontroller might actually begin or continue operating. It could even send out well formed commands over SPI or I2C or RF; in a few situations that could be problematic - you think a system is off but it continues to function. Probably not often a concern, but if we are ever working with systems where having the microcontroller operate when we think it's unpowered could be a problem, it's good to be aware of the possibility of it operating under "phantom power" supplied via an input pin.