The bug

Minimizing the game whilst being in a singleplayer or multiplayer world causes the game process to start eating up RAM until it has reached full usage of the memory allocated to the JVM. This makes the game become very unresponsive, forcing the user to kill the process via Window's Task Manager. If the user reopens the game shortly after minimizing it, there is a chance that the game will clear up some memory and proceed as normal. Please note that this only happens if the game has loaded up a singleplayer/multiplayer world before; the memory usage does not increase if the game gets minimized in the main menu.

How to reproduce

1. Monitor the game process in Window's Task Manager (javaw.exe)
2. Join any singleplayer world / server
3. Press ESC on your keyboard to pause the game
4. Minimize the game
5. Watch how the process' private bytes increase over time

Video showing the bug in action on YouTube

Original description

I was playing minecraft in fullscreen and then I pressed escape to pause it and windows key to minimize it. Then I realized that minecraft would slowly use more and more RAM, up to 4.2GB (I allocated 3GB), When it reaches 4+GB it stops climbing then drops after 5 seconds to 500MB and then starts climbing again. When I try to bring it back to play it it takes up to 10 seconds to appear on my screen. After that everything works fine.
Video: https://www.youtube.com/watch?v=KZ0HlSv6zbM