Second hint;

#19: In one of the game modes, you can freely drive around. If you reach the edge of the map, there's a tall cliff blocking you from going out of bounds. There's still a way to get up there though, and when you do, then it happens.
#19 (Hint 2): You and your bike will get blasted away from the cliff halfway across the level accompanied by the loud sound of a cannon blast.

We breach the top 20.

21- This game is the first in the series to introduce a new kingdom to the fray. This new kingdom was much needed to flesh out the late game, as it can be quite lonely to be the only person of note in a sea of nobodies.

20- This game is fairly new, it features an interesting combat system with 4 stances and many items, skills, and spells to add. As well as some bonuses when picking a certain patron to represent you.

19- This game is the third in a series simply about collecting treasure and hoarding it. In order to do that you ruthlessly put down anyone in your way with horn or fire.

Still not a single guess on this one. Let's make it a little easier then:
#19:
-A long time ago humans destroyed themselves by creating machines that used biological matter to create more robots, which happens to include humans as well
-The main character is a clone of a woman who lived almost 1000 years before the events of the game
-An open world game set in the distant future, where world has been largely taken over by robots and humans are mostly confined to small isolated settlements

Hmm, I thought that already with the last hint, but as I never played said game I thought someone else might know better. But if by now there are no takers I wager the guess, that this sounds like Horizon Zero Dawn. Not sure about the clone-thingie (or other stuff), as I didn't play it, but the things I know about the game match these hints. Maybe it's completely wrong. Who knows.

#20 - Dead Space 2: I love the entire trilogy, but Dead Space 2 is something special. The gameplay, the graphics, the soundtrack, the ambientation... Everything in this game works really well with the horror theme. To be honest, I don't really like the zero gravity segments, but that's something very small compared to everything the game offers.

#19: Astral Chain

Correct.

Damn, got myself spoiler-ed from reading those hints. Guess it's my fault for not finishing it after BotW came out. 

So to summarize.

20. Lunar: Eternal Blue Complete (unguessed)
19. Lunar: Silver Star Story Complete (guessed by Liquid_Laser)
18. Final Fantasy VI (guessed by Darashiva).

Next three:

17. The philosophies of Friedrich Nietzsche and Carl Jung, and giant combat mecha.

16. A guy and a girl battle against an ogre queen and a weapons merchant trying to drum up a global war.

15. You must protect a college student from a cult of Spanish zombies.

#15: Resident Evil 4