The big problem with your classic video game hud ((Take Halo for instance)) is that it assumes a stiff, static posture. Your aim with never vary with a crosshair, but I know several people who can shoot effectively without aiming. Pistols, for instance, were considered point and shoot weapons and you weren't really supposed to aim wth them. This is why the iron sights are so small. They were there if you needed them, but they weren't exactly the greatest. Instinct shooting was a better skill to develop with them.
One place where instinct shooting is used is in those arcade games. The sights are always off, and you are constantly trying to get a feel for where the shot will actually go. Proper positioning, and position consistency is key with this.
The whole reason a crosshair was developed in the HUD was to allow people to play the video game and know where the bullets would be going. A good game that did not really encorperate this HUD system was 007 Golden eye for the N64. People would tape a dot to the screen because that was where the bullet would go, or you could ADS and you would get a red cross hair. Not exactly perfect, but it instilled the same sort of skills.
Ammo count, equipment on person, IFF, Vitals, and other such things however would be great for a HUD system as it leaves information directly there for you to see. A system showing you where the gun is aiming would be best if you had a system like the corner shot, where you can't exactly see what you are aiming at with your own two eyes would be effective.