Any game that lets players proceed at their own pace is fine with me. I enjoy the rather linear Prince of Persia series because I can normally take the time to take in my surroundings and take time to carefully observe the challenges in my way. I don't exactly feel the same way about rollercoaster rides like Call of Duty or any game trying to shove me along through a series of story scenes as if I'm an actor in a movie, as opposed to letting me appreciate the narrative when I feel ready.
On the other hand, I adore the Metroid series for letting me ignore much of the story. I can scan items in Metroid Prime to glean a few details that capture my imagination, or on my tenth playthrough I can focus on speedrunning through the game's cleverly designed, interconnected levels. Even the more linear Metroid games (I'm looking at you, Prime 3) are still fine in my book, as long as the narrative presented still leaves enough for me to imagine or find out on my own (Other M... and Fusion to a lesser extent). Most of the games in the series are pretty good at visual and audio storytelling, too. The atmosphere is astounding.
Replayability can be an issue for most linear games though, so my final answer is non-linear.
3DS Friend Code: 0645 - 5827 - 5788
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