Ori and the Blind Forest?

As Liquid Laser guessed correctly, the game #19 is Fire Emblem: Radiant Dawn.

This was the first Fire Emblem game I played as I got into console gaming with the Wii. And it is quite cool. I like the tactical gameplay of all Fire Emblem titles (and similar titles as well), so that is a given. But there was more here. The Laguz are quite cool switching into their beastform, these are much more seldom in other titles.

The 3D-representation of this title was OK, it didn't take away from the overview over the battlefield (3D if made wrong can be bad for the overview, 2D usually works well for these titles). It was fun leveling the units while taking care to lose none. This made me sink in hours and hours. So it makes the list.

Wikipedia, MobyGames, OGDB, IGDB

game #15

Hint 1: Combine materials gained from slaying monsters to get magical stones.

Hint 2: It's a spinoff of a long-running series (that started in the 80s).

Hint 3: As you fulfill quests the tavern gets emptied.

Hint 4: Deep in the labyrinth is a ... waterfall?

game #14

Hint 1: Poisoning the environment is setting the events in this game into action.

Hint 2: A time-traveling toilet.

Correctly guessed by The_Liquid_Laser: Day of the Tentacle.

game #13

Hint 1: You die in the tutorial.

Correctly guessed by The_LIquid_Laser: Demon's Souls.

game #12

Hint 1: Play as a goddess and fight an old beast.

Time for more hints

#16 This 80's arcade game could be described as Minecraft with a bicycle pump.
Hint 2: This game was in Stranger Things 2.
Hint 3: The title of this game is two verbs. One of the verbs is the past tense of the other.
Hint 4: In this arcade game you dig through the ground while defeating enemies by dropping rocks on them You can also inflate them with a bicycle pump until they blow up.

#13 This mobile game is a sequel to tower defense game where you have to grow your defenses to repel an undead horde.

#12 This is the spiritual successor to a PS3 game, This game also has 2 sequels and a spin-off game.

#27
Hint 1: Shows off the capabilities of the system, you don't even need to use buttons!
Hint 2: Microgames.
Hint 3: Wario
Hint 4: Ware
Not Game & Wario, not Warioware Smooth Moves.

#23
Hint 1: 99
Hint 2: It's an early 3D game.
Hint 3: 1998

#20
Hint 1: Shells & Banana Peels 3D

#19
Hint 1: Party time on your handheld system.

#18
Hint 1: Sequel to #23.

#17
Hint 1: You can be a tree?!

#16
Hint 1: The only real sequel in the whole franchise.

#15
Hint 1: It's a fresh and original game.

15 and 16 are correct. 20 is close. 17 though, not quite

16: Namco's Dig Dug, ah the memories.

13: Kingdom Rush 2?

12: Dark Souls

Ocarina of Time, Mario Party Advance/DS/Island Tour (take your pick) and Majora's Mask respectively.

All correct (it's Mario Party DS).

Metroid Prime?