What resources are (technically) finite in Minecraft?
Most resources in Minecraft are infinite. Plants regrow, animals reproduce, mobs respawn. water sources can also become infinite, based on their placement. Even stone is infinite through the combination of flowing lava and water, and then smelting.
But there are some resources that do not have a natural "reproductive" quality. Eg, lava cannot replace another source block like water can.
What other resources in Minecraft do not have this quality?
According to the Minecraft Wiki category for non-renewable resources:
Ancient Debris Block of Diamond Budding Amethyst Coal Ore Cobweb Conduit Copper ore Dead Bush Deepslate (and derivatives) Diamond Diamond Ore Dragon Egg Dragon head Elytra Emerald Ore Enchanted Golden Apple Enchantment Table Gold Ore Heart of the Sea Horse Armor (except leather) Iron Ore Jukebox Lapis Lazuli Ore Minecart with TNT Nether Quartz Ore Netherite and all Netherite-derived items Netherite block Netherrack Raw Copper Raw Gold Raw Iron Redstone Ore Sand Sandstone (and variants) Sponge TNT
Note that this list is not perfect; the original from the wiki contained some PE exclusive blocks (I have edited these out), and it may not contain all items from the 1.9 update of Minecraft. I have also removed items unobtainable in the survival mode inventory.
If you find any more, or feel that a block should be added/removed from the list, please feel free to edit this post.