I don't think Spike/Acquire's unusual action game Way of the Samurai has ever been widely known or very popular, but I think it is a game which does a lot of interesting things with its story and game flow. Most notably, it is a game which embraces both interactivity in the plot and a very movie-like style, and combines both with a lot of replay value.
In terms of the main combat system of the game and other elements of being an action game, it is not outstanding in any respect. The combat system has its variations and a few good mechanics that keep the game interesting, but a few annoying ones (like the difficulty in acquiring special moves and ease with which you can break swords). As an action game, the game is mediocre to average, at best. However, the action elements are just part of the real nature of this game.
As a whole, this game is about choosing your path through a story. In each scene of the game, there are countless things you can do, and each choice has a distinct impact on the plot. Most importantly, these decisions are not merely prompts asking you for a limited number of written options, since simply ignoring an plot event is often possible, and you can often choose from many events simply by choosing where to go at any particular point in time. Also, at almost any time in the game, including the middle of many story sequences, you can just draw your sword and start attacking people, and the plot will respond accordingly. This last element gives the game an unrivaled fluidity between story and action, so the player almost never gets pulled out of the sense that he is in control of the character's actions and identity.
You can see a great example of the variety of choices open to the player in the very first scene. Here, right when you start the game, you see a gang of thugs in the process of kidnapping a young woman. The first option is to simply walk by them without saying anything, and pick one of the two different roads to take to different areas (and different scenes). The next option is to speak to the thugs, and choose from one of the dialog choices, which results either in a fight or the thugs tying the hero to some railroad tracks. Another option is just draw your sword and provoke a fight with the thugs. Finally, you can just wait around a bit until another character shows up and starts a fight (and I only know if this one from FAQs). Based on what happens here, you can get introduced to characters on completely different sides of the central conflict and see the story from very different perspectives. I consider this one scene to be one of the best moments in all of the videogames I have ever played, and it is just one of many similar scenes with different outcomes.
The plot of the game is built on the idea that there is a certain set series of events that will occur, and that the will of the player is the only variable that can alter these events. In fact, one of the characters comments on this, and asks the main character to leave the area in order to prevent him from interfering with what will happen. The player can observe and alter every major event in the plot (though not every event in one playthrough, of course), and these choices affect the rest of the plot and change the ending. This is not implemented perfectly (the final sequence, the battle against the military invasion of the area, is mostly the same in every plot path and can't be avoided), but it lets the player understand the situation and deliberately act to try to control known future events, which is greatly empowering.
The consequence of having a game with so many flexible choices is that the game is very short on each playthrough. It is rather easy to finish the game in one or two sittings. But at the same time, the game has a lot of replay value, and the game developers have introduced a few things to make multiple playthroughs more fun. The ability to collect the swords of your opponents, and then improve those swords and bring them into the next playthrough of the game, is a nice touch that lets you try new fighting styles and combat strategies, even when going through the same fights from a previous playthrough of the game.
Way of the Smaurai is not a perfect game, but it does many things to create a great sense that the player is the character he is controlling, and has the power to influence the game world just as a person in that world should be able to do. It provides an immersive game with a lot of freedom.