A mix. I don't want to keep track of every HP and spell slot, so that my challenges are fairly presented and fairly defeated. But I have a hard time NOT memorizing everything my players can do. It's like a narrative running in the back of my head like "Player A could do this, and this, and then Player B could do that, and still have enough left over for the next challenge."
I try to turn it off, and just enjoy the moment. Success varies.
Vaguely, yes I do. I am not tracking every hit point or spell slot, but I keep aware of generally how beat up they are, or if they are running low on magical oomph. As GM, whether I like it or not my choices have a lot of impact on the pacing and mood of a session. I prefer to make those choices informed.
I'd like to say true, but there's a glaring exception where the system demands that I do it. Specifically when players engage in rest overuse to 5mwd nova and I need to make the adventure react to avoid a 2-3hr session being completed in tens of minutes
There's a couple of resources I personally keep track of as I find them the most crucial from behind the screen:
1) Hit Dice. Seems silly to do, but knowing how much recovery your party can get during a short rest can tell you whether they're gonna take one or not. If a series of events have burned their hit dice while the long-rest characters still have most of their resources, there's a good chance they'll skip a short rest unless the warlock begs.
2) Healing Items. How many are still in play because a forgotten healing item can result in an anticlimactic PC death because of a faulty memory. "Hey, Tim? Go ahead and roll intelligence for me." Tim rolls a 15 "You could probably save Thag with that healing potion you got two months ago from the Swamp Witch's Hovel. Yeah, the mossy green potion no one wanted to drink 'cause it smelled like swamp water."
As I said in the other thread: the world is organic--it is what it is. The PCs interact with it as best they can, but it makes no difference to me how many spell slots, hit dice, or uses of a feature a PC might have remaining when I plan an encounter--the encounter is planned according to the narrative of the world/story and the world-building itself.
For example, tonight was a harsh night for the PCs. Two were killed outright by a critical hits after their hp was reduced, another was knocked unconscious, and the other two fled. An NPC was also killed (but by the party LOL!). Their resources were fair, but they should have run, only one tried before going unconscious.
Anyway, the encounter was there because it made sense for the world-building that it be there. That is all that matters, for me, anyway.
I went back and forth on the question. In the end, I can't say that I don't pay any attention. I would like to not pay any attention, but I play with a lot of new players IRL, and I play PBP here, where I have generally not been able to leave it up to the players to track. Mostly, I can trust them, but not all will keep track. Of course, I can't be trusted to keep track either (I'm notorious for losing saves), so I figure between the bunch of us, it'll work out close enough to correct.
With my home group, I don't pay any attention, though.
I find it interesting that most people seem to interpret this statement to mean "I don't keep track of the PCs various remaining resources like hit points or spells slots," but it seems at least one person has interpreted it mean "I handwave stuff like how many rations or pieces of ammunition they have left" (and thus voted false).
I generally don't care how many charges a character has left on their magic item, Hit Dice, or uses of an ability before a long rest. The exception to this is if I suspect a player is themselves not paying attention. Not so much with regular arrows - I really don't care about ammunition, unless it's magical.
Now, one way I do care is if I know they're running low on HP, spells, and whatnot, I might softball an encounter a little. Unless they've spent their resources alpha-striking. Then that's on them and they'll have to take their lumps.
In the last thread I said how I plan encounters based on what the party is capable of, so I have to know what all they can do. In this one I answered true, because I'm not responsible for whether they over or underuse those resources, so I really don't pay attention to them. If they are too free with those resources and run out before they hit a hard encounter, they are going to be in trouble.
I have a general sense of their hit points, and I stay aware of when they've blown major resources like high-level spells, wildshape uses, rages, etc. I pay slightly closer attention if the players are novices; not because I think they'll cheat, but just to make sure they're aware of the rules.
when I want to play resource games I play StarCraft. I keep a running tab of what they should have. (it may or may not be completely accurate) The only time I pay attention to individual resources is when it's for extremely exotic things like components for a wish spell or some such thing.
I play on a VTT and even though I rarely look at the PC character sheets, the initiative tracker includes a graphic showing how low each character's HP is.
Listing to the Glass Cannon podcast (GCP) is making me want to turn this off. In the GCP the players don't tell the GM their HP. As a GM I like this. Part of the fun is not being completely in control of the story. Sure I'll have an idea of which PCs are in trouble, but not knowning the exact number would make things more interesting for me as the GM.