As the most common block (air and water notwithstanding) in the game, and as someone who digs in mountains a lot, I have the most of it compared to any other block. I use it a lot, but I have the most of it still too. It either goes into storage or I toss it.
I keep a chest of it, after that it gets smelted into stone and fashioned into stone-based blocks for availability. Anything after that goes towards filling in caves going outwards from base. As I play modded I dislike the disorganization of random caves slashing through my pretty basebuilding on the minimap.
I use cobble and stone for making stable bridges and walkways in the Nether. In deserts I use them to stabilize cave ceilings. I usually make stone bricks out of cobble because they look nicer to me. In the overworld I use all kinds of stone and wood to make rustic paths. In my last world I built a network of sturdy rustic paths between every single village I found. It is very time-consuming but they look nice when decorated with trees, leaves and fragments of fences.
The Meaning of Life, the Universe, and Everything.
I always have a full stack on me for survival purposes (makeshift bridge, stairs, etc), while I generally keep it stored (often smelted with excess charcoal). I often build things out of stone bricks, or usually make some attempt somewhere at having a floating island because they always look cool.
I use all of the cobblestone I collect while caving, such that I rarely accumulate more than a stack in my inventory; if I tend to get more I'll place more, such as in the holes left behind by ores mined out; conversely, if I'm collecting less I'll be more likely to place a torch in those spots instead; likewise, if I'm exploring along the edge of a ravine I'll mine/place cobblestone as needed to make the ledges passable. I also collect cobblestone when branch-mining for resources early on, and while digging tunnels for railways later on, which is all eventually used up while caving (I'll bring several extra stacks in my ender chest) or used to build bases (this included my main base earlier on, now I use quartz, which itself is mainly a product of mining it for the XP), with no more than a single chest of cobblestone stored at my main base.
I actually use quite a lot of cobblestone, with 608,000 stone mined and 757,000 cobblestone placed in my first world, including 162,000 which was mined and placed again, making it my second-most placed block by far, only surpassed by torches:
In my modded worlds I use even more cobblestone due to the more complex caves, including using it to pillar up and make scaffolding to access the ceilings of large caves (this shows that I've also crafted 1360 cobblestone, due to using my mod's "compressed cobblestone", which compresses 4 cobblestone into one block; this was cobblestone that I accumulated while mining the rail tunnel to my most recent base, all of which was used up in building the base itself and while caving):
Cobble from early game gets mostly used up for mob grinder and initial nether exploration. Once I get a silk tough pick, I pretty much stop gaining cobble. I mine only stone which gets used for various projects. (Mostly in form of bricks) Occasionally I need a lot of observers or droppers/dispensers, so I specifically need to go digging for cobble.
I store it, even the excess can be used for something later on. I find uses for it one way or another
be it making safe tunnels through the nether, or building structures in the overworld.
a little trick I've always used with my stone nether tunnels in older MC worlds is making a half slab window on the sides, so Ghasts, Blazes and Skeletons can't cause trouble.
Bases in the nether are less useful now though, no thanks to the fact Piglin will cause you aggro the minute you open a chest in front of them when it wasn't even theirs to begin with. On top of this Piglin can spawn just about anywhere in the nether, although usually in Crimson forests.