Minecraft Running Out of Memory

Whenever I open a world, the game doesn't load anything, and player falls to y=8, appearing in survival (health bar, armor, hunger bar), before it quits and comes up with a screen that says "Minecraft has run out of memory."

Steps to recreate:
1. Open a world in the snapshots.
2. Play on that world.
3. Open world in 1.6.1 pre.
4. Open it any time after.