[nrlucas]

"Within a week, trees were in short supply."

If you're implying minecraft in general, then yes. Otherwise in this particular case, resources seemed to be all finite.

[Sukotto]

The following things are "infinite" if you forbid exploration into new areas:

* Water

* Lava Flows (Sources are finite)

* Wood/charcoal: if you have enough saplings and dirt.

* Cobblestone: if you have lava and water in the correct arraignment

* Wheat: if you have enough seeds and dirt

* Fish: if you have water

* Neutral-Monster items: for those monsters you can breed if you maintain the habitat

* Aggro-monster items

I believe that's it

[jlgreco]

There are a few random others. Apples should be infinite, since they come from trees. Other plant-ish things as well, like melon or pumpkin, provided you have any in the first place.