Sting sings the works of John Dowland. Dowland has been called the first singer/songwriter (he was a singer accompanying his own melancholy, lost-love songs on lute) in English, and had a very interesting life. He was a roman catholic who was not in favour at court because of this, and was forced to travel Europe, at one point being the court composer of King Christian IV of Denmark. He was also accused of being involved in a plot on the queen's life (though I seem to recall that he actually was central in foiling a plot on a protestant nobleman earlier in his life, I can't find any evidence of it).
Actually, the first singer-songwriters that we know of were probably Sappho and Arkhilokhos. They played their own songs on the lyre, which is where the words "lyrics" and "lyrical" (and "lyrikk" in Norwegian) come from.