Song melody
 

So when composing a song, who is usually given the melody. It seems that the singer will always sing the melody of the sung, but I'm wondering if the other instruments usually play along. For simplicity, let's say that this is for a singer singing along with one guitar or piano.
It seems like this might make for a boring song if both the instruments and the singer are both playing the same notes overlapping each other.
Or does the accompanying instrument just play the song's chord progression and maybe playing the melody with the singer to add emphasis at certain parts?
Thanks.