I'm playing on a local server to test the new 1.7 snapshots. The other player on the server never had the same issue. Basically, when I sometimes open my inventory (starting with 13w42a/b snapshots), the game instantly crashes. I can now only play for a few minutes without the game crashing, and at some points I couldn't even figure out how to play anymore since the game kept on crashing each time I relogged and opened my inventory.

I don't know what is exactly the cause of this bug, hence I am unable to provide the steps to reproduce the bug, but I hope the crash log will give you enough information.