I'm planning on upgrading my GPU but I was also wondering if I should switch out my current am2+ Phenom II x4 940 and 4 gigs of DDR2 800 for a Phenom II x4 965 with 4 gigs of DDR3 1333. How substantial will the performance increase be in that case?
I would not worry about upgrading to the Phenom II X4 965 and DDR3 RAM. You'll see little performance increase... Comparision - There is not of enough of a difference to warrant the cost increase.
You'll be better off spending on the money on a better GPU (or dual setup) or possibly adding a SSD to your system, along with the new GPU.