I was driving home yesterday listening to a Steve Forbert CD. "Romeo's Tune" (a song I love and that he dedicated to the memory of Florence Ballard, late of The Supremes) came on. I started singing with it. I do a pretty dead-on imitation of Mr. Forbert on that particular song. A friend once commented on how eerily I capture his sound.
Similarly, I do a pretty decent imitation of Elton John on "Candle in the Wind" - the one from the Live in Australia album, not the one from Goodbye Yellow Brick Road; I find the former has more emotion than the latter.
Even if a song is not in my key or my range I can transpose and still sound at least a little like the artist. For example, I tend to sing harmony rather than lead on early Beach Boys songs.
When do I sound the worst? When I'm singing 'cold,' without a recorded reference. In other words, I can sing like other people, but I can't really sing like me.
I think this is because I learned to sing from the radio and from records. My goal was to sound like the artists I was hearing. If I were serious about learning to sing I'd hire a teacher, learn to read music, and learn to sing like me.