Has this started happening again after you updated to the latest drivers? I still think you should remove/uninstall GeForce Experience.

I removed geforce experience, and this problem started months ago(I talked to EVGA support and we couldn't fix it, so I RMA'd the card, and it worked fine for a while), and the past week it has become unplayable. Before if I would just close TwitchTV on my second monitor, I could play Overwatch just fine. Now I will sometimes crash within 5-10 minutes of playing it. I will also revert back to older drivers and test it when I get home later today.

How do you play a game on one Monitor and watch TV on a second Monitor without being Killed in the Game?
You should go back to 368.81 for now and do some testing.
Being that the Old Card had this issue and your New Card has this issue it seems to me that it is an issue with your MB and or PSU.
But because the GTX 660 is kind of old you could test with driver 327.23.

2 GB isn't a whole lot of VRAM and might be causing problems running a graphics intensive game plus a second monitor with it. There are some games that I play on my GTX-980 Gaming 4G boards that will cause my GTX-680 2 GB to lock up and crash.

It has been crashing while I play one game as well now. I had Overwatch open (lowest settings), and nothing else, and in 40~ minutes it crashed my PC.

I shut my PC off before I left this morning, and when I came home I played WoW for over an hour straight (nothing else), and my game froze, went black, for about 5 seconds, then turned back on. Then 10~ minutes later it froze completely. I restarted, and within 15 minutes it froze and went black again.
 
I tried the old drives yesterday, and am using the newest drives right now.

CrunCherTiMe
I have a GTX 660, and recently I started having a weird problem where my monitors will go black, and then sometimes go back to normal, or they will go black and then say HDMI/ DVI (Dual monitor) and my computer stays on, but I can't hear sound or do/see anything.
 
It's a new card (the old 660 had the same issue though).
 
Any ideas?
 
Thanks.

Sounds like a faulty gpu to me. How long did the new card work before having issues again like the old card? Can you test the card in another system (family, friends, pc repair shop)? Does the crashing go away when using integrated graphics?

The new card had similar problems, after a few days. It wasn't as bad as it is now,at first it would just freeze for a second or freeze then go back to normal.

Time to request an RMA replacement I think.

Update: I removed one ram stick, and it crashed(although it seemed to have lasted longer than usual, could just be a placebo thing). But I then took out the other ram stick and put the first one I took out back in, and so far I haven't had any crashes in over 8~ hours. I'm going to test it a bit more just to make sure though. And if it works fine I guess the one stick of ram is bad.