One of my favorite examples of this is Dreams by Fleetwood Mac, but that may be because I've been practicing it on harmonica.
The song begins (with note names and relative major scale numbers):
Now here you go again
A C D E D C
6 1 2 3 2 1
(low)
But that's not how Stevie Nicks sings it. She starts the word "go" very flat, not quite all the way down to the Eb, but maybe 70 cents down from the E? And then she slides up to the E from there. Listen to her sing it and you will know what I'm talking about.
If you have an instrument where you can play either the straight notes or the notes with that slide, play it both ways and you will hear the difference.
This song is fun and easy to play on harmonica, including the pitch bends, if you get or make the right harp. You need a High C Melody Maker, which you can order from Seydel or you can take a Lee Oskar F Major and retune it into a C Melody Maker: raise the blow 3 from C to D, and raise the draw 5 and draw 9 from Bb to B.
How do you retune a harmonica? You file the reeds! Take off some weight near the free end of a reed and it will vibrate faster, giving it a higher pitch. More strangely, you can also lower the pitch a little by thinning the reed near the fixed end.