Virtual novels as I saw someone mentioned I like, but only if they have enough choices.
Those with no choices suck usually.
Two of my favourite games are Life is strange, and life is strange before the storm. It's almost it's own genre though.
Long story is a cute mobile game also with choices.
I actually almost forgot about the games! Life is Strange and Before the storm are two of my favorites, as well as Detroit: Become Human, Until Dawn and Heavy Rain.
What I like about the latter three specifically is that the ending for them isn't set in stone. One of Life is Strange's biggest problems is that when it comes to the end, you're left with an A or B type of option, which pretty much means all of your choice making meant absolutely nothing. Even Before the Storm, though it was slightly more opened, had to close itself off to connect with the original LiS.
With Heavy Rain, your ending can change depending on different circumstances. Each character has different ways of developing throughout (specifically the original protagonist), and it feels like your choices have a little more weight.
Until Dawn, that feeling gets pushed up just a bit with the added fact that none of the 8 controlled characters are guaranteed to live throughout the game. I mean, sure, games have twists and turns and character deaths...but how many games have been made up to this point to where nobody outside of the antagonist(s) is guaranteed to live or die?
On top of that, it was really nice to see how your choices affected personality traits of the controlled character, as well as their relationship with the character they were interacting with. It really added to the ending, to where characters would talk about each other fondly if you built up good relationships between them...or talk angrily about them if you chose actions such as saving yourself and leaving them to die.
It just made the ending that much more interesting since, unless you beat for beat made the exact same choices, no runthrough was guaranteed the same result.
Detroit then amped that up even more by introducing basically a choice chart: a chart that showed the choices that you made as well as what the result was that you triggered. Like Until Dawn, none of the three characters were guaranteed to live (in fact in one of the beginning scenarios, it's incredibly easy to make the wrong choice and get the character killed). But on top of that, it felt like your choices had so much more weight to them.
Again, they led up to really neat endings, while not as intricate as U.D's many MANY different types of endings, still felt like your choices were what really affected the end result.
Really, if Dragon Age refined the choice/consequence system a bit and looked at these games for inspiration, Dragon Age could really be a force to be reckoned with...same with Mass Effect. Both series have massive potential that was squandered by their 3rd games (most of your choices barely carrying over to Inquisition, M.E giving you a basic A-B-C choice ending).
With Dragon Age: Dread Wolf Rising being announced, I really hope they take a page from some of the more refined choice mechanics out there.