The player should never/sometimes/often run out of ammo.
Which statement makes sense? Continuing on the nostalgia trip of my examination of Doom's E1M1, I think of how those early games turned me into an ammunition miser. (Was it the game? Was it, as my brothers and I now wonder at now, peer reinforcement about Dad's fiscal conservativism?)
I remember finishing the first episode of Doom with 95% of the rockets I picked up through the levels, taking down the Barons with excessive zeal. Finally, I could spend those rockets because there's no way to keep them after the last level. I hoarded ammo because I might need it, and unlike many modern shooters, actually running out of ammo was a real possibility.
Maybe it put a crimp in my fun--that BFG-9000 unfired until the Cyberdemon showed--but maybe ammunition conservation is it's own kind of fun, it's own mechanic and reward system.
It's a game sub-system that modern shooters with infinite pistol ammo largely forgo, which is a shame. When gamers are continually re/over-supplied to their hearts' content, the strategic long-term questions about rationing or expenditure recede entirely as does challenge.
I would argue that it undercuts the modest yet crucial roleplay that comes with a shooter: I'm a space marine, I'm a Rainbow 6 operative, I'm whoever Call of Duty calls me to inhabit, and to a man every one of them should be mindful of their ammunition.
I think of every time I've needed the Hammer of Dawn in Gears of War, well low and behold, here one is conveniently dropped and I feel like a chump for keeping a weapon around that is guaranteed to be given to the player again if he ever needs to use it.
More simulative shooters give the player realistic ammunition loads but also restrict information about exactly how many rounds are left: SWAT 4, Red Orchestra come to mind.
Killzone 2 has the option to reduce or eliminate the HUD entirely, something I enjoy tremendously. I'm only about halfway through that game, but I have never once truly needed to know how much ammo I have left. (Though proprioceptive/body awareness cues advanced creatively would be appreciated, like being able to look down at a chest harness and see remaining full magazines.)
Not to say there aren't modern games that consider and tweak the modern conception. Mirror's Edge is a wonderful example of more or less bypassing weapons and ammunition entirely; they are of limited use to Faith. If the player chooses to use them, Faith stops at stooping to reload the things, giving them a temporary power-up like quality. But that is dispensing with weapons, not really reconsidering ammunition useage.
A better example would be more traditional survival horror games, such as old Resident Evil titles, which severely restricted available ammunition. Adherents to this first games generally crabbed at the relative surplus of ammunition available to Leon in RE4 and then later to Redfield and Sheva in RE5, though it's still scrounging by the standards of many games.
As with so many modern shooter paradigms, I think it's Far Cry 2 that has come out with a fascinating balance to this question. Using your own weapons usually means you can stay well stocked, though sometimes with supply runs to the weapons depot; the far more interesting risk/reward mechanic is picking up rusty weapons off your fallen foe. There is a kind of economy of bad-assedness which dictates that your super killer mercenary character should be able to pick up any guns he comes across and kill with it, increased weapon jams and all. And taking his malaria pills in time.
But I can't help but think there might be some more interesting spaces to be explored with very limited ammunition loads, or artificially scarce ammunition, like the aforementioned Detective game concept. Or maybe a game that would play like a sort of no-tech Crysis--instead of playing the super soldier Predator-ing around an island with armed thugs looking for him, it's more of a Manhunt scenario where the player can--and should--use every dirty trick in the book to take down his target. Six bullets, six targets?
Playing a game version of Cormac McCarthy's The Road, where only one round left is an even grimmer proposition than usual?