Electrical tape is my go-to. Complete blockage and is made to stick to plastic and metal.

I'm surprised it worked for you. I have an Asus N66W router with 5 blindingly bright blue LEDs. Being in my bedroom, it made it really hard to sleep.

Placing three layers of electrical tape didn't work, the light still passed, although significantly dimmed, through the tape. Also, because the router's case is thin plastic, most of the light leakage was through the case. The only solution was to put a pillow over the entire thing. But in the morning the router had overheated and didn't work until resetting it.

Nowadays I just unplug the router before going to sleep. It's driving me insane.

Although it's not an issue as it lives in a cupboard, my ASUS RT-AC68U has a switch on the back which completely disables all of the LEDs. Also to their credit, even though the LEDs are blue, they're not of the obnoxiously bright variety.

I suggest metal foil under easily removable adhesive tape (e.g. paper masking tape, which is also available in suitably wide formats).

Your electrical tape could be tough and insulating, but it's still basically transparent plastic.

Already posted in another comment, but these "LightDims" stickers work perfectly for me. They also have different colors to blend in with various cases: http://a.co/7KaPIM2

No affiliation, just recommend them to everyone when I have the chance!

Yup. Sharpies work great. I had to do exactly that to the otherwise-excellent air filter that I keep in my bedroom.

I really like opening it up and putting a sheet of tinfoil over the LED, with a single pin-prick hole.