Okay thanks for the detailed response. Over the past couple days I have tried the tests you recommended.
I passed the memtest86+ 9 times. I also passed the memory diagnostic tool. I never swapped any components though.
I also have been running the Driver Verifier for the past couple of days.
Here is a zip with the crashes I have had since I have been running the verifier.
Thanks again for all your help so far. I have noticed the crashes are becoming more frequent and outside of video gaming.