I just recently had a scary situation where I thought my computer totally died. Turns out it didn't, but it made me want to back up my save files to my Dropbox in case anything ever happened, since I'm like 60 hours in and losing all that would suck.

I'm not sure where to find the save files - I checked the BGII directory in the "GoG.com" folder in my Program Files x86 location, but I don't see a "saves" folder in there. Does anyone know where I can find my save files to back up?

They are where ever you installed the game. Both the Baldur's Gate and the Baldur's Gate 2 folder contains a folder named "save".

I checked the directory that I installed to and there's a bunch of stuff there but no "saves" folder. I took a screenshot and everything - the folder just isn't there: http://i.imgur.com/Gq5uo.jpg

I checked the folder options to make sure hidden folders were viewable; didn't think a saves folder would be hidden but I thought I'd try anyways. The same is true of my Torment directory, no saves folder there either. I'm really stumped.
Ah ok it turns out I have to click the "compatibility files" button at the top, for some reason. But looks like I'm all set now. I appreciate your help!

Okay... I assumed it was the same in all versions of the game (I do not have the GOG version). In that case I would search for "000000000-Auto-Save". That is the subfolder of the Auto Save. Should be in the same folder as any other saves. Unless that is different as well... ;-)

Take a look at this post, in all likelihood it's the same issue.

Also it's good practice to install your games, especially old ones, in a folder other than Program Files, to avoid problems such as this.

I found my games in My Documents. Hope that helps!

Correct,they are found in my docs.