I seem to have the minority opinion, but... Finite ammo and ammo weight was something important in [for instance] the original Fallout RPGs. In those games you could get your hands on a powerful minigun or flame thrower, but the ammo for those guns was HEAVY stuff, and it often came to making the choice of hauling extra tanks & boxes of bullets ~or~ bringing along a few rockets, and/or dropping some equipment. Part of it is the very need to switch weapons when the ammo runs out, or when something goes wrong with the weapon. Take the early shooters for [prime] example. Unlike todays FPS [with common ammo drops from corpse looting], the early shooters treated their levels almost like a puzzle, and often doled only just [barely] enough ammo to get through them. Conservation of ammo was a must, and was part of surviving the maps. Getting stuck with no ammo was a real concern for the uncareful. In Doom/Blood/Duke/SW/... you might have to get by with melee attacks until you could find more ammunition; and you were careful when you got some.
I am not a fan of unlimited conventional ammo; in either endless quantity or in uncounted carrying capacity. In EoB, it could be a pain to hunt down arrows, but it was genuinely nice when you found new ones to replace the ones you'd lost, and/or allowing you more shots than before.