My preferred alternative to electrical tape is a piece of aluminum foil stuck on with painter's masking tape. Aluminum foil (or any metal) is really excellent at blocking all the light, and painter's tape doesn't leave residue.
I used to run a Dell UltraSharp 3008WFP. A great monitor for the time, but the power LED was so damn bright that black electrical tape didn't fully extinguish it.
If you don't want to see the LED you can cover it with electrical tape.