Internet is full of "GOG.com Promo Codes" and similar codes. As an example, you can see the following link (please be careful, I suspect this to be a scam):
www.greenpromocode.com/coupons/gog-com/?c=55085
Do these codes work or is it just a scam? If they work, how do I use them?

They are normally not a valid thing. Gog either discounts a game so that everyone can buy it cheaper or in a few cases it is tied to games you already own, meaning there is also no code and your account is checked. The only thing gog has are giftcodes for games or for a certain amount of money in a few cases. But the first ones you should not buy on other sites since they are from resellers (which is not allowed in gogs user agreement) and sometimes they were bought with stolen credit cards meaning the game can be just removed from your account. And the later codes are very rare, just given out in a few contests, so they are not really around and seeing someone trying to sell them etc would be really suspicious of being a scam.

What's interesting is that the NEWFOR code seems to try to gift Worms World Party Remastered, but then it won't let you proceed. I wonder when the promo was and why haven't we heard from it.

Yup. Maybe it was some kind of Team17 promo.
Because that code won't gift you Worms World Party Remastered but will apply DISCOUNT ON IT.

Just like Blackguards code. Gave you a reply on your reddit post too.

Ah, you're probably right :).

Hm, the code I still have on my Guacamelee! Gold edition seems to disagree with that. It is a single use code though, and will expire sometime in September.
The Strike Suit Zero discount code for the Director's Cut though seems to not be expiring, yet I still think it's a single use code.

Curses! Foiled again! True, I do not recall getting any discount codes from other sites, though there were a few third party giving bonus codes for games. Not selling gift codes, but distributing bonus ones, like for Kickstarter rewards.
But yeah, rule of thumb is that any codes floating around are bogus ones.

Wait, you mean that you guys won't ship me my games for free?!
That does it! You'll be hearing from my lawyers!

You joke, right now someone over at EA is working on charging for that. :P

I think an explanation like this should have it's own thread, and then stickied.

That's just, like, my opinion, man.

GOG have partnered with internet service providers the world over to make sure your games are safely shipped to your location. Additional costs may apply for said service, depending on the provider in question and how hard a bargain they drive.