Running LED tape on an inappropriate power supply.

A very common power supply used in LED lamps is a little switchmode power supply that is designed to put out a current of around 300mA at between about 3V to 12V to drive 1 to 3 1W LEDs in series.
If you connect these supplies to standard LED tape with multiples of three LEDs in each section, then the power supply will drive whatever length of tape you connect to it, but the voltage will adjust down until the full 300mA is shared between all the LEDs.
This means that for a 5m roll of tape the current will be divided between 100 circuits of 3 LEDs giving just 3mA per circuit.
That's actually enough to run the tape brightly for visual effect, while ensuring it has a long lifespan due to being under-run.

There are a couple of caveats though.
If an LED goes short circuit then the voltage may be pulled down to the rest of the LEDs as it passes more than its share of the current.
If the tape breaks then the 300mA will be shared amongst the remaining LEDs, and for a very short section it could overdrive them.
There is no guarantee of proper mains isolation with these tiny switching power supplies. They are intended for closed lamps, so there is a risk that the LED tape could be referenced to the mains.

This was done purely as an experiment.