Carole King was part of a large stable of songwriters who were mostly expected to write songs for others to sing. She wrote a lot of songs we associate with other acts (partial compilation here). Then, in the late '60s, she became part of the singer-songwriter boom (James Taylor, Elton John, Gordon Lightfoot, many more), where artists lived out the fact that the way to have your songs done right is to do them yourself.
But of course, we don't believe a Carole King song is really a Carole King song until it's covered. A lot. So here's Dusty Springfield.
And if she were here, I bet Barbra Streisand would tell us she wishes she hadn't worn that oddly decorated bustier.