I have had several issues with my MacBook Pro in the last year or so. At completely random times when I'm using it, it will shut down in one of about four ways. The screen will either change to just one color (has been pink, yellow, green, orange, blue, black, etc), the whole screen will be filled with small horizontal lines of varying bright colors, a box will come down telling me that my computer needs to restart, and to hold the power button if it does not automatically, or it will turn an off-white color and have what looks like code along one side. It usually comes up with a report after it restarts. I've taken it to the Genius Bar several times, but it never crashes while it is there, so no one can help.

Any idea what this could be? It usually doesn't happen very often, once or twice a week, but lately it has been getting worse.

From the symptoms you gave it seems that the video chip on the logic board is going out, which would require a logic board replacement to fix. Some places like blueraven.com will repair the laptop for a flat rate, somewhere around $400-450.

What Jim said. I went through exactly the same thing last summer with a 5 yr old Macbook Pro. Time for a new machine, I'm afraid.