Graphics glitch that turns the world into fractured, repeated images

What I expected to happen was...:
Normal minecraft game play with normal graphics.

What actually happened was...:
I log in to any server at all and the environment is broken into pieces that shift and change repeated segments every time I move. All sounds are still normal and I can feel the real environment around me, but it's like trying to play the game while blind.

Steps to Reproduce:
1. Start playing on any server

I don't know how or why this is happening. Is it a problem with my computer? Sometimes after not playing for a while I can get back online and have normal graphics again, but I've been coming across this problem often.