For the last two months, while just browsing the 'net the driver will stop and then restart, about every 3 or 4 days. I just looked at the Event Viewer before posting here, and it shows 72 instances, all at the same time, of a generic "nvlddmkm Event ID 13" error. The card runs flawlessly in-game however. What can I do to stop this from happening? 
 
Thanks for any help. 

More than likely, the card is slightly unstable (due to age/deterioration) when in 2D hardware accelerated mode.

Options available to you:
1) Try different drivers. Driver version 347.25 is most recommended for that age of card. Newer drivers tend to not work as well for older 'End of Life' video cards.
2) You could modify your video card's BIOS (will void warranty) to increase voltage slightly in the 2D performance state. I myself had to do this just recently with my GTX 580s.
3) Disable hardware accelerated graphics/video in your browser (this is an option in most browsers somewhere in the advanced properties menus).
4) Use the program NVIDIA Inspector to accomplish item 2 above without voiding your warranty (but will require having NVIDIA Inspector to always be running).
5) RMA the graphics card.

Good luck!

After installing the 353.38 patch driver, my internet pages are loading faster. I predict this is what the issue was, since the TDR's were mentioned there as well. 
 
Thanks again, Saijn, and thanks to you, ty_ger for your help as well.