I have a decent PC, with an intel i3 CPU, 3 GBs of RAM and a 1 GB GDDR3 128-bits graphics card.
I can run MC just fine, getting over 60 fps most of the time. I noticed that when the memory usage of MC gets close to 1 GB, it started to freeze for 2 seconds then coming back and repeating the cycle. Only solution I seemed to find was restarting the game itself.
My guess is that after going through all those landscape elements, the used memory starts to build up and the game chokes (does that make any sense?).