There are two in particular that have consumed my life for the past half year: Hatoful Boyfriend and Zero Escape.
Hatoful Boyfriend - I don't know if anyone around here has played it, but for those who haven't, you're gonna have to bear with me on this one. HB is first presented as a dating sim where you play as a female human who is attending a school for birds, and yes, your choices of dates are all birds. That part of the game is meant mainly as a parody of dating sims, but it introduces the cast and gives some foreshadowing for the main event.
The game is hilarious, heart-wrenching, and everything in between. I've played it through several times now and I still end up a blubbering mess every time. The characters, the story, everything is just so well-written;
I very quickly forgot that most of the cast were birds. XDDD I went in thinking it would just be something for me to laugh at and make fun of, but I got so, so much more than I ever expected.
Zero Escape - This comprises the two games 999 and Virtue's Last Reward. These games are more well-known so I won't get into them too much. Once again another wonderful example of writing, and holy shit can they ever pull off plot twists. My mind has been so utterly screwed by these two games that it took a good amount of time just for what actually happened to sink in.
Honourable mentions go to the Ace Attorney series (my first love!) and Holiday Star (HB sequel that was recently released). And who's excited for Zero Escape vol. 3!??!!