When I GM I lean more toward keeping track, but it ultimately depends on the type of game I'm going for and what the players want to play. If it's a one shot deal I'll let things slide, but for an angoing campaign that I'm going to spend a lot of time on, I'm going to constantly edge people toward keeping track. Back when I played regularly most of the guys a ran with were pretty into guns in real life, and wanted the game to be more realistic, so yeah, we kept track of every bullet, every clip, where it was stashed on you or in your safe house, even to the point that people would declare they were emptying clips and putting the bullets in fresh clips so the springs wouldn't get messed up from being compressed all the time. The changing the clips thing out was their idea, but knowing what you had and where was mine. I grew up/cut my RPG teeth on Dark Sun, so managing limited resources has always been sorta second nature. The last time I played, it was me and some guys playing a one shot as everyone happened to be in town for christmass, and there was no keeping track whatso ever.
As a player, I have a seperate sheet of paper (normally a few) to keep notes durring the game. NPC names, locations we go to, objectives for the mission, stuff I pick up and stuff I use along the way. This is where I keep track of ammo/clips. At the end of the session, I go through and update the original character sheet and either crumple and toss the scratch sheet, or if there's room use it again for next session.