Non-Renewable Resources are items that can be run through completely; no more will spawn after world generation. For example, although it is extremely hard to do so, it is possible to run out of ore in a select area, but since the worlds are unlimited you can only run out of ores in the area that you live in.
List (does not include crafted items)
- All mineable blocks except Stone, Cobblestone, Monster Eggs (not special Stone Brick), Leaves, crops, Snow, Snowballs, or Wood products.
- All items obtained from blocks except the ones above (unless already a mob drop, i.e. Redstone Dust, Gunpowder, Gold Nugget, and Glowstone Dust).
- Nether Stars.
- All Potions except those obtained from Witches.
Cobblestone, and therefore Monster eggs and stone, is impossible to run out of due to the fact it can be created by water and lava, in a cobblestone generator, for example.