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Buy this to get Original War Legacy version

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Buy this to get Neighbours From Hell 1+2

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Buy this to get Sam & Max Save the World (2007 Original Version)

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Buy this to get Wolfenstein II: The New Colossus German Edition
Thanks to @Lone_Scout for reporting this.

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Buy this to get Crystal Caves

This thread also maintained a list for games that Supports original look and feel in remastered version.
Does Crystal Caves HD qualify for the list?

Alwa's Awakening should be removed from the list.

Done, thank you!

TIME-LIMIT
Customers who pre-order this version of System Shock will receive System Shock 2: Enhanced Edition for free when SS2:EE is released.

Time-limit:
If you pre-order Warhammer 40,000: Battlesector until 13th May 2021, 5 PM UTC, a free copy of the cult game Master of Magic will be added to your library.

https://www.gog.com/game/warhammer_40000_battlesector
https://www.gog.com/game/master_of_magic

Time-limit:
The premiere of The Amazing American Circus - The Ringmaster’s Edition is set for 12th August 2021. It will consist of the base game, OST, and Ringmaster's Essentials DLC. Until the day of its premiere, The Amazing American Circus - The Ringmaster’s Edition will be available on GOG.COM at the price of the base game.

https://www.gog.com/game/the_amazing_american_circus_the_ringmasters_edition
https://www.gog.com/game/the_amazing_american_circus
https://www.gog.com/game/the_amazing_american_circus_official_soundtrack
https://www.gog.com/game/the_amazing_american_circus_the_ringmasters_essentials

Time-limit:
When you buy BIOMUTANT in our store, GOG will gift you a complimentary copy of Shadow Warrior 2 Standard Edition. The serial key to redeem this game will be added to your GOG library automatically after purchasing Biomutant (please select the game in the library through your browser, then click "More", and finally enter the “Serial Keys” section).

This offer is available until the 1st of June, 2021, 5 PM UTC, yet the serial key you acquire thanks to it stays active until you redeem the game at any time in the future. Users who pre-ordered BIOMUTANT before this special offer has launched will receive the serial key for Shadow Warrior 2 Standard Edition at no extra charge.

Quite a few Bethesda games don't include TES Arena and Daggerfall.

Those are:
Wolfenstein: The Two Pack
Prey (both editions and the DLC)
Dishonored: Complete Collection
Wolfenstein II: The New Colossus (both editions)
Arx Fatalis
Wolfenstein: The Old Blood
The Evil Within & DLCs
Wolfenstein: The New Order
The Evil Within 2
Dishonored®: Death of the Outsider™
Dishonored - Definitive Edition
Dishonored 2
Wolfenstein II: The Freedom Chronicles (all 3 episodes and the season pass)

All other games do include TES Arena and DAggerfall.

Time-limit:
When you buy MechWarrior 5: Mercenaries in our store, GOG will gift you a complimentary copy of The Surge! The serial key to redeem this game will be added to your GOG library automatically after purchasing MechWarrior 5: Mercenaries (please access the “serial numbers” section of the library through your browser).

This offer is available until the 2nd of June, 2021, 12 PM UTC, yet the serial key you acquire thanks to it stays active until you redeem the game at any time in the future.

Fixed, thank you!

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Buy this to get Witchaven (Original)
Buy this to get Witchaven II: Blood Vengeance (Original)