Hi Magne! There is already a ready-made feature at the editor, on the right click menu: "Paste Unformatted".
Good to know
If you want "Paste Unformatted" to be done when the user presses CTRL + V, take a look at this forum post. http://world.episerver.com/Forum/Pages/Thread.aspx?id=15981&epslanguage=en. I am using it in every project, and it works like a charm :)
Thank you Tore! That was a good solution!