It all depends on the game, but I find that while the shotguns or the rocket launchers are shiney and pretty, the TRUE hero gun of any FPS is the trusty, crude-yet-effective one that pulls you through 90% of the game's difficult encounters. And in a good majority of recent FPSes, this has been the staple Assault Rifle.
A good assault rifle is accurate and powerful; though she may not shoot exceptionally fast, she puts forth the hurt needed to stand tall in a world of shiney boomfest weapons, and she shines her brightest in the absolute most fun combat range: middle range. Short range is usually simply won by the guy who holds down the trigger and runs sideways while jumping and crouching, and while sniping requires skill, it's a lot less risky since your targets often can't get a good shot back at you. But at mid-range, it often comes down to who can balance dodging and being unpredictable with firing accurately and effectively. These are the true tests of skill.
However, I do have to give mad props to the Shotgun from F.E.A.R. That thing is just plain sexy.