The vocal melody of the song is what sticks with most people; and in many cases is what makes them like or dislike a song - whether they realize it or not.
If your melodies are well-written and catchy, people will remember and enjoy your music. If the melodies you write are carelessly written and bland, they won't. It's that simple.
Try putting your music to the test; imagine you are hearing your music being played as muzac at your local shopping mall. No lyrics, no guitar riffs, just a syrupy string section behind a trumpet playing the melody. How does it sound? If a melody is strong, a song should sound good, no matter what style it is played in.