Vinegar will do it - to a point. Proprietory descalers will usually work until all the limescale has gone. In my experience vinegar works until the temperature of the water drops too far - but never the less it does work.
BUT - be wary of leaving the kettle boiling - I'm not sure what it may do the the element. (I have found it best to boil it and then switch it off and leave it for 15 minutes or so before re-boiling)
Also be careful of the fumes - vinegar is an acid and I assume the fumes are likewise - consider putting the kettle under an extractor fan.
If your kettle is white plastic it is possible that the plastic may stain brown.
By the time you have spent money on the vinegar and the electricity you may have found it cheaper to use the de-scaling tablets!