I've been pondering about this for a while, for me it's fairly simple;

1. A nice, steady pace with some progression along the course of the song.
Example: Five Finger Death Punch's The Bleeding with a guitar duet instigating the song, then there's the introduction of the bass followed by the drums, rhythm guitar and lastly lead guitar before getting into the main part of the song.
2. Live drums as they just sound better and give songs a raw sound that you just don't get with electronic drums.
Example: the first snares 1:27 into Green Day's Wake Me Up When September Ends.
3. Meaningful lyrics that convey a message to make you feel something or coax an emotional shift.
Example: Again being Green Day's Wake Me Up When September Ends, the story of Billie Joe's father dying of cancer and the first words Billie Joe said on the day of his father's funeral as he stormed to his room.
4. Choruses that aren't the same or as frequent, 3 is all that's needed in a song at maximum.
Example: Linkin Park's Breaking the Habit, two being the same is moderately fine but it's the change in the final chorus that gives a nice feel to the end with Chester's habit being understood leading to him breaking it.

What about you?