Also developed by Quantic Dream, Beyond: Two Souls plays very similarly to Heavy Rain. Where it does differ is in its plot, which deals with more supernatural tones. Either way, if you dug David Cage's work, you'll likely enjoy this.
It's been a few years since Quantic Dream has released a game, but Detroit: Become Human is set to finally release in 2018. It's an intriguing look at the future, and hopefully will be able to push storytelling in games.
Bioware is one of the most popular developers in gaming today, and their work on the Dragon Age series has been top notch. The most recent title, Dragon Age: Inquisition, continues the series' tradition of allowing players to change the course of both story and character arcs through their choices. Players will have to play through Inquisition multiple times to experience all it has to offer!
While morals may largely be largely gone in the apocalypse, Fallout 4 still deals with plenty of dilemmas. Major choices will have to be made, and consequences will have to be suffered. It is worth noting that Bethesda has made other great choice driven titles in The Elder Scrolls series, such as Skyrim and Oblivion.
Dontnod Entertainment showed a lot of promise with 2013's Remember Me, but really came into their own as a developer with the episodic game Life is Strange. It features one of the most touching stories in all of gaming, and was one of the best surprises of 2015. The prequel, Before the Storm, is also out now.
If you enjoyed playing detective in Heavy Rain, then you'll dig Murdered: Soul Suspect. It has the interesting twist of figuring out your own murder as a ghost, and players get to pull off some Ghost Trick-style shenanigans.
Sherlock Holmes: Crimes and Punishments is an interesting case, as it actually allows the player to throw perfectly innocent suspects into prison. This kind of tension, and not penalizing the player for wrong choices, puts the player in the fictional detective's shoes. This is developer Frogwares' best take on Sir Arthur Conan Doyle's famous sleuth.
Telltale has a done a great job in revitalizing adventure games, and The Wolf Among Us is the best story they've told. A second season is on the way, so this is definitely the best time to jump in. If you don't like fairy tales, Telltale has also made similar games based off other popular properties such as Borderlands and The Walking Dead.
One of gaming's best stories can be found in the Zero Escape series. Choices definitely matter in the series, but it differs due to the fact that players will have to replay the same scenes to see how the different choices would've played out to get the full story. All three titles are worth playing.