Will I know some games from GoG and Steam use older versions of DosBox. And I was wondering, how would I update. I've tried the 'copy & paste'(the .exe that is), and that didn't work, as I got an error.

You can't really upgrade DosBox for some GOG games from what I know as they're specifically configured for a certain version of DosBox. We had this issue discussed some time ago when someone wanted to install a game but use a newer version of DosBox and the installer didn't allow it.

You don't need to upgrade DosBox in the traditional sense but can keep both the old and the new version installed next to eachother. What you can do is this:
a) Install the new version of DOSBox in another folder
b) reinstall the GOG game that uses DOSBox but right before installation, pick to choose the DOSBox folder
c) pick the folder of the new version
d) overwrite the game folder itself (backup configuration files first if you want)
e) play with the new version!
I've always used the latest CVS or RC of DOSBox with GOG and it has never given me any issues.

I updated correctly my previous installations of GOG's games to DOSBox 0.74, just unzipped the new ver files over the old ones, it works flawlessly.

Doh, now I feel like a dumbass. I never realized DOSBox frontends existed, so to get my GOGs working in Mac OS, I had created my own XCode project template for making .app DOSBox wrappers for each game.

D-Fend Reloaded is Windows only, but you can find a list of other frontends (including ones for OS X) right here on the DOSBox wiki.

http://boxer.washboardabs.net/
Does basically the same thing, except they're *.boxer instead of *.app.

Yeah, Boxer is the one I found when I Googled "DOSBox frontend" after reading Carlos' post. I had gone full out, creating my own Cocoa launcher and everything (to choose between game, client/server and setup exe's, and expansions if applicable), only to find a much more polished version just a short google away.
Well, at the very least I learned something doing it myself, right? Right? :P

Indeed. I'd prefer learning how to do something only to later learn that I don't have to, than not having learned how.