For archival purposes and what not. Only includes demos released in North America. If anyone wants create a list of all the European and Japanese demos go right ahead.
The list:
Resident Evil Revelations Demo (30 Uses - 1/19/2012)
Mario & Sonic at the London 2012 Olympic Games (30 Uses - 01/26/2012)
METAL GEAR SOLID Snake Eater 3D Demo (30 Uses - 2/16/2012)
Nintendogs + cats Demo (10 Uses - 2/16/2012)
Crush 3D Demo (30 Uses - 3/1/2012)
Mutant Mudds Demo (30 Uses - 3/29/2012)
Pyramids Demo (30 Uses - 4/19/2012)
Rayman Origins Demo (30 Uses - 5/17/2012 - Removed from the eShop on 7/12/2012, but returned on 11/1/2012)
Order Up!! Demo (30 Uses - 5/31/2012)
LEGO Batman 2: DC Super Heroes Demo (30 Uses - 6/6/2012)
The Amazing Spider-Man Demo (10 Uses - 6/14/2012)
Kingdom Hearts 3D Dream Drop Distance Demo (30 Uses - 6/21/2012)
Rhythm Thief & The Emperor's Treasure Demo (30 Uses - 6/28/2012)
Heroes of Ruin Demo (30 Uses - 7/5/2012)
Theatrhythm Final Fantasy Demo (Unlimited Uses - 8/30/2012)
THE "DENPA" MEN: They Came By Wave Demo (30 Uses - 9/20/2012)
Style Savvy Trendsetters - Fashion Contest Demo (5 Uses - 10/4/2012)
LEGO The Lord of the Rings DEMO (30 Uses - 10/11/2012)
Moshi Monsters: Moshlings Theme Park DEMO (30 Uses - 10/18/2012)
Marvel Pinball 3D Demo (30 Uses - 10-25-2012)
Style Savvy - Trendsetters Shopping Spree Demo (30 Uses - 11/1/2012)
Disney Epic Mickey: Power of Illusion Demo (30 Uses - 11/8/2012)
Fractured Soul Demo (10 Uses - 12/6/2012)
Adventure Time: Hey Ice King Why'd you steal our garbage? Demo (5 Uses - 12/13/2012)
Art of Balance TOUCH! Demo (30 Uses - 12/13/2012)
2 Fast 4 Gnomz Demo (30 Uses - 12/20/2012)
Fire Emblem Awakening Demo (30 Uses - 1/17/2013)
Brain Age: Concentration Training DEMO (30 Uses - 1/24/2013)
Etrian Odyssey IV: Legends of the Titan Demo (30 Uses - 2/7/2013)
NARUTO Powerful Shippuden Demo (30 Uses - /2/14/2013)
Monster Hunter 3 Ultimate Demo (30 Uses- 2/21/2013)
Sonic & All-Stars Racing Transformed Demo (15 Uses - 2/21/2013)
Castlevania: Lords of Shadow - Mirror of Fate Demo (30 Uses - 2/28/2013)
Pokemon Mystery Dungeon: Gates to Infinity Demo (30 Uses - 3/7/2013)
HarmoKnight Demo (10 Uses - 3/14/2013)
Project X Zone: Imperial Demo (5 Uses - 6/4/2013)
Project X Zone: Ghost Demo (5 Uses - 7/2/2013)
CRAZY CONSTRUCTION Demo (30 Uses - 7/4/2013)
Undead Bowling Demo (30 Uses - 7/18/2013)
THE "DENPA" MEN 2: Beyond the Waves Demo (30 Uses - 7/18/2013)
Chain Blaster Demo (30 Uses - 7/25/2013)
Mario & Luigi: Dream Team Demo (12 Uses - 8/11/2013)
Etrain Odyssey Untold: The Millennium Girl DEMO (30 Uses - 9/16/2013)
Phoenix Wright: Ace Attorney - Dual Destinies Demo (30 Uses - 10/1/2013)
Witch & Hero Demo (30 Uses - 10/3/2013)
AiRace Speed DEMO (30 Uses - 10/31/2013)
LEGO Marvel Super Heroes: Universe in Peril Demo (30 Uses - 10/31/2013)
Sonic Lost World Demo (10 Uses - 11/15/2013)
Nano Assault EX Demo (30 Uses - 12/12/2013)
AeternoBlade DEMO (30 Uses - 12/12/2013)
Brunch Panic Demo (30 Uses - 12/19/2013)
World Conqueror 3D Demo (30 Uses - 12/19/2013)
Bravely Default Demo (30 Uses - 1/2/2014)
Jump Trials Supreme Demo Version (10 Uses - 1/9/2014)
Chibi-Robo!: Photo Finder Demo Version (15 Uses - 1/9/2014)
WAKEDAS Demo (30 Uses - 3/13/2013)
Conception II: Children of the Seven Stars Demo (30 Uses - 3/25/2014)
I am an Air Traffic Controller Airport Hero Hawaii Demo (10 Uses - 3/27/2014)
Mario Golf: World Tour Demo (15 Uses - 4/24/2014)
THE "DENPA" MEN 3 The Rise of Digitoll DEMO (30 Uses - 5/8/2014)
Gardening Mama 2: Forest Friends Demo (5 Uses - 5/8/2014)
Alien On the Run Demo (10 Uses - 5/22/2014)
Quell Reflect DEMO (30 Uses - 5/26/2014)
Toy Stunt Bike Demo (30 Uses - 5/26/2014)
Tomodachi Life Demo (30 Uses - 6/2/2014)
Jett Rocket II Demo (30 Uses - 6/10/2014)
Cubit the Hardcore Platformer Robot Demo (30 Uses - 6/31/2014)
Cooking Mama 5: Bon Appétit! Demo (5 Uses - 7/14/2014)
THEATRHYTMN FINAL FANTASY CURTAIN CALL DEMO (30 Uses - 8/4/2014)
Bit Boy!! ARCADE Demo (25? Uses - 8/4/2014)
Glory of Generals Demo (30 Uses - 8/4/2014)
Parking Star 3D Demo (30 Uses - 9/11/2014)
Super Smash Bros. for Nintendo 3DS Demo (30 Uses - 9/19/2014)
Color Zen Demo (5 Uses - 10/2/2014)
Sonic Boom: Shattered Crystal Demo (8 Uses - 11/5/2014)
European Conqueror 3D Demo (30 Uses - 11/13/2014)
Fishdom H20: Hidden Odyssey Demo (3 Uses - 11/20/2014)
AiRace Xeno Demo (30 Uses - 11/27/2014)
Ohno Odyssey Demo (20 Uses - 11/27/2014)
Special Demos/Misc:
Tomodachi Life: Move-in Version (Unlimited Uses - 5/19/2014 - Given away to select Club Nintendo members. Two codes were also bundled with the full game.)
Super Smash Bros. for Nintendo 3DS Special Demo (Unlimited Uses - 9/12/2014 - Given away to select Club Nintendo Members)
Pokémon Omega Ruby and Pokémon Alpha Sapphire Special Demo Version (Unlimited Uses - 10/21/2014 - Given away through various promotions. More info.)
The list:
Resident Evil Revelations Demo (30 Uses - 1/19/2012)
Mario & Sonic at the London 2012 Olympic Games (30 Uses - 01/26/2012)
METAL GEAR SOLID Snake Eater 3D Demo (30 Uses - 2/16/2012)
Nintendogs + cats Demo (10 Uses - 2/16/2012)
Crush 3D Demo (30 Uses - 3/1/2012)
Mutant Mudds Demo (30 Uses - 3/29/2012)
Pyramids Demo (30 Uses - 4/19/2012)
Rayman Origins Demo (30 Uses - 5/17/2012 - Removed from the eShop on 7/12/2012, but returned on 11/1/2012)
Order Up!! Demo (30 Uses - 5/31/2012)
LEGO Batman 2: DC Super Heroes Demo (30 Uses - 6/6/2012)
The Amazing Spider-Man Demo (10 Uses - 6/14/2012)
Kingdom Hearts 3D Dream Drop Distance Demo (30 Uses - 6/21/2012)
Rhythm Thief & The Emperor's Treasure Demo (30 Uses - 6/28/2012)
Heroes of Ruin Demo (30 Uses - 7/5/2012)
Theatrhythm Final Fantasy Demo (Unlimited Uses - 8/30/2012)
THE "DENPA" MEN: They Came By Wave Demo (30 Uses - 9/20/2012)
Style Savvy Trendsetters - Fashion Contest Demo (5 Uses - 10/4/2012)
LEGO The Lord of the Rings DEMO (30 Uses - 10/11/2012)
Moshi Monsters: Moshlings Theme Park DEMO (30 Uses - 10/18/2012)
Marvel Pinball 3D Demo (30 Uses - 10-25-2012)
Style Savvy - Trendsetters Shopping Spree Demo (30 Uses - 11/1/2012)
Disney Epic Mickey: Power of Illusion Demo (30 Uses - 11/8/2012)
Fractured Soul Demo (10 Uses - 12/6/2012)
Adventure Time: Hey Ice King Why'd you steal our garbage? Demo (5 Uses - 12/13/2012)
Art of Balance TOUCH! Demo (30 Uses - 12/13/2012)
2 Fast 4 Gnomz Demo (30 Uses - 12/20/2012)
Fire Emblem Awakening Demo (30 Uses - 1/17/2013)
Brain Age: Concentration Training DEMO (30 Uses - 1/24/2013)
Etrian Odyssey IV: Legends of the Titan Demo (30 Uses - 2/7/2013)
NARUTO Powerful Shippuden Demo (30 Uses - /2/14/2013)
Monster Hunter 3 Ultimate Demo (30 Uses- 2/21/2013)
Sonic & All-Stars Racing Transformed Demo (15 Uses - 2/21/2013)
Castlevania: Lords of Shadow - Mirror of Fate Demo (30 Uses - 2/28/2013)
Pokemon Mystery Dungeon: Gates to Infinity Demo (30 Uses - 3/7/2013)
HarmoKnight Demo (10 Uses - 3/14/2013)
Project X Zone: Imperial Demo (5 Uses - 6/4/2013)
Project X Zone: Ghost Demo (5 Uses - 7/2/2013)
CRAZY CONSTRUCTION Demo (30 Uses - 7/4/2013)
Undead Bowling Demo (30 Uses - 7/18/2013)
THE "DENPA" MEN 2: Beyond the Waves Demo (30 Uses - 7/18/2013)
Chain Blaster Demo (30 Uses - 7/25/2013)
Mario & Luigi: Dream Team Demo (12 Uses - 8/11/2013)
Etrain Odyssey Untold: The Millennium Girl DEMO (30 Uses - 9/16/2013)
Phoenix Wright: Ace Attorney - Dual Destinies Demo (30 Uses - 10/1/2013)
Witch & Hero Demo (30 Uses - 10/3/2013)
AiRace Speed DEMO (30 Uses - 10/31/2013)
LEGO Marvel Super Heroes: Universe in Peril Demo (30 Uses - 10/31/2013)
Sonic Lost World Demo (10 Uses - 11/15/2013)
Nano Assault EX Demo (30 Uses - 12/12/2013)
AeternoBlade DEMO (30 Uses - 12/12/2013)
Brunch Panic Demo (30 Uses - 12/19/2013)
World Conqueror 3D Demo (30 Uses - 12/19/2013)
Bravely Default Demo (30 Uses - 1/2/2014)
Jump Trials Supreme Demo Version (10 Uses - 1/9/2014)
Chibi-Robo!: Photo Finder Demo Version (15 Uses - 1/9/2014)
WAKEDAS Demo (30 Uses - 3/13/2013)
Conception II: Children of the Seven Stars Demo (30 Uses - 3/25/2014)
I am an Air Traffic Controller Airport Hero Hawaii Demo (10 Uses - 3/27/2014)
Mario Golf: World Tour Demo (15 Uses - 4/24/2014)
THE "DENPA" MEN 3 The Rise of Digitoll DEMO (30 Uses - 5/8/2014)
Gardening Mama 2: Forest Friends Demo (5 Uses - 5/8/2014)
Alien On the Run Demo (10 Uses - 5/22/2014)
Quell Reflect DEMO (30 Uses - 5/26/2014)
Toy Stunt Bike Demo (30 Uses - 5/26/2014)
Tomodachi Life Demo (30 Uses - 6/2/2014)
Jett Rocket II Demo (30 Uses - 6/10/2014)
Cubit the Hardcore Platformer Robot Demo (30 Uses - 6/31/2014)
Cooking Mama 5: Bon Appétit! Demo (5 Uses - 7/14/2014)
THEATRHYTMN FINAL FANTASY CURTAIN CALL DEMO (30 Uses - 8/4/2014)
Bit Boy!! ARCADE Demo (25? Uses - 8/4/2014)
Glory of Generals Demo (30 Uses - 8/4/2014)
Parking Star 3D Demo (30 Uses - 9/11/2014)
Super Smash Bros. for Nintendo 3DS Demo (30 Uses - 9/19/2014)
Color Zen Demo (5 Uses - 10/2/2014)
Sonic Boom: Shattered Crystal Demo (8 Uses - 11/5/2014)
European Conqueror 3D Demo (30 Uses - 11/13/2014)
Fishdom H20: Hidden Odyssey Demo (3 Uses - 11/20/2014)
AiRace Xeno Demo (30 Uses - 11/27/2014)
Ohno Odyssey Demo (20 Uses - 11/27/2014)
Special Demos/Misc:
Tomodachi Life: Move-in Version (Unlimited Uses - 5/19/2014 - Given away to select Club Nintendo members. Two codes were also bundled with the full game.)
Super Smash Bros. for Nintendo 3DS Special Demo (Unlimited Uses - 9/12/2014 - Given away to select Club Nintendo Members)
Pokémon Omega Ruby and Pokémon Alpha Sapphire Special Demo Version (Unlimited Uses - 10/21/2014 - Given away through various promotions. More info.)