Right at the moment, I don't have time to look at all the entries and decide which one I like best. So this giveaway will probably run until monday.

The video for Peter Gabriel's hit "Sledgehammer" of 1986 contains famous examples of claymation!
I remember another music video which used that technique, but unfortunately I can't recall the song title nor the singer's name. It was an old-fashioned, maybe really old song (think about a jazzy, "big band" sound, with brass), it was sung by a colored singer with a very characterful, at times almost falsetto voice, can you name it? "Uh... ah.... uh... ah..." "O - o - o - o.... o - o - o - o...." "rrrrrrrrrriiiii" etc.

This one? (even if I don't think so, because it doesn't match the rest of your description)
Or this one? (which is really a classic jazz song)

Can't find the video, but wasn't it - Marvin Gaye - I Heard It Through The Grapevine?

No, it most certainly wasn't. But thank you for trying.

Let me just add that the mysterious song is in a much faster tempo than that. It has really a bouncy swing.

OK I finally managed to find the video on YT... the song is called "Reet Petite" and it is an oldie, it's from 1957 and the singer is Jackie Wilson.
The video is obviously a more recent production, although I don't know who made it nor when it was made; I remember having seen it as a child. Well, actually I associated an unpleasant feeling to it, even if I couldn't exactly tell why. Now, after seeing it again after many years, I know the reason. Yes, it is technically poor, it's butt-ugly to be more precise, but it's more than that. It really is the stuff of nightmares. Words fail, you have to see it to understand. Don't you say I didn't warn you. Watch at your own discretion.

https://www.youtube.com/watch?v=xJ3-NnNx6Zs

Not in, just wanna say yes very yes to The Mysterious Stranger and Celeb Deathmatch

I wonder if you guys have seen these shorts done by Aardman for DC Nation called "DC's World's Funniest". To enjoy them you need a bit of context as Aardman used real children to voice the superhero characters by tailoring the questions to get the desired responses and thus creating charming, compelling characters which are not so super. The results are adorably hilarious though as you can observe in the five 1 min. shorts.

Episode 1: www.youtube.com/watch?v=VF1VK1aUsNo

Episode 2: www.youtube.com/watch?v=bJMJVhM31sI

Episode 3: www.youtube.com/watch?v=fscj7sW856w

Episode 4: www.youtube.com/watch?v=8DjpdB77354

Episode 5: www.youtube.com/watch?v=SEpa9dev7-Y

Countdown BUMP!

First of all a big thank you to everybody who contributed something to this giveaway. I absolutely loved every video that was posted and found a lot of stuff that I didn't know before and it was a tough call to choose a winner. I wish I'd have more than the one code to give away.

In the end I will give the Wallace and Gromit game to KasperHviid for the Happiness of the Katakuris video (and also for the other interesting links and infos he provided).

Congratulations!

Congratulations to you, KasperHviid! *claps* I hope you enjoy your game! :D

Thanks again for the giveaway PaterAlf and this thread as it has been a lot of fun watching all the cool claymation videos. Congrats to KasperHviid on getting to play an obsolete game, hopefully it will return to GOG someday along with some other great games that were also removed. :)

Holy cow .... I won? I WON! Thanks, this is grand! :-) Also, thanks to everyone in this thread for contribution to this nice collection of claymation vids. BTW, here's what I could find of claymation games wishlisted on GOG:

The Neverhood
The Dream Machine
The Dark Eye
Platypus
Platypus II
Skullmonkeys
Clayfighter
Clayfighter 63
Clayfighter: The Sculptors Cut
Clayfighter 2: Judgement Clay
Clayfighter: Tournament Edition
Clay Agent
Claymates

As cose_vecchie mentioned, GOG already has the gothic scifi claymation horror puzzler The Swapper (okay, it is not claymation as such since the animation itself is digital, but all visual element are hand-crafted in clay, and it looks fantastic!)

Interestingly enough, I couldn't find any claymation game that didn't have a wishlist. This proves that claymation is cool.

Okay, except NUX. That one didn't have a wishlist. but that one can be bought on bigfishgames.com

Thank you PaterAlf for this giveaway, one of the most original and brilliant seen so far, and congratulations to the winner!
But... do you really mean the above for every video? Even the last one I posted? REALLY?

Congrats, KasperHviid, and thanks again, PaterAlf!