You can use a solution of vinegar and water to descale your kettle (unless, as hobodave mentioned, the manufacturer advises against using vinegar).
Fill your kettle with water until it's half full; add about 1/2 cup of vinegar to the water, and then allow it to boil for about 10 minutes.
Allow the water to cool and unplug your kettle.
Gently scrub away the scale with a non-metallic pad (don't scrub the heating element if it's exposed;
wipe that with a sponge).
Rinse your kettle several times after removing the scale, and then boil one or two fillings of water in it to ensure that you remove all traces of the vinegar.
cooking.stackexchange.com/users/403/Iuls
I've found that citric acid works best.
You put it in a kettle of boiling water, and just let it do its magic.
It cleans up any plaque buildup, and brings it back to a shiny pristine state.
Works much better for me than vinegar, for some reason.
cooking.stackexchange.com/users/505/Jono
I have generally found the vinegar method to be suitable and haven't heard of anything specific as to why it would be harmful.
Vinegar is usually only about 5% acid solution so rather weak as far as acids go.
A lot of manufacturers will recommend a specific cleaning solution because it's yet another thing that you have to buy from them.
You should be able to find descaling solutions in cleaning aisle of the grocery store or visit your local restaurant supply store for descaling solution.
cooking.stackexchange.com/users/426/Darin Sehnert
Follow the manufacturer's directions.
I have heard the vinegar thing for coffee makers too, but it's not a universal thing.
Specifically, my coffee maker has very explicit warnings about not using vinegar, or any other acidic solution to clean it.
Instead it suggests soap and water for the externals, and a vinegar-free descaling solution for the internals.
I don't own an electric kettle, but I wouldn't be surprised if some models had prohibitions or warnings of their own.
I know for sure they will have specific instructions in their manuals though.
For anything electric/electronic that you care about, follow the instructions.
cooking.stackexchange.com/users/60/hobodave
Vinegar and baking soda work fine to clean kettle.
You can find the formula here
cooking.stackexchange.com/users/55414/Nicky
If you don’t want to use white vinegar, you can use apple vinegar.
I have tried it in my kettle with pure apple cider vinegar.
It worked very well too.
cooking.stackexchange.com/users/45543/Sarah
I have an electric kettle that I clean by scrubbing the insides with plain water. I was wondering if there was a better way to clean it. I remember hearing somewhere that you can clean a coffemaker by running a solution containing vinegar through it and was wondering if there might be a similar solution to clean the kettle?
How to clean an electric kettle?
cooking.stackexchange.com
<cleaning><kettle>
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cooking.stackexchange.com/users/27/Kyra
Unless otherwise advised by the manufacturer, a vinegar and water solution, citric acid or vinegar and soda can be used. Apple vinegar can be used instead of white if preferred.  You can use a solution of vinegar and water, citrid acid or baking soda to descale a kettle.
You can use a solution of vinegar and water, citrid acid or baking soda to descale a kettle.