So, you're playing a game and you're confronted with some challenges. Do you prefer those challenges to be straightforward and have them take you through the game, or those challenges to be complex and give you optional challenges leading to multiple paths in an open world?
I personally like to play nonlinear games more because I feel like I'm actually going somewhere and doing something. Free to go wherever I want and not having to just stick to a certain path, even if there is a suggested one. Even so, there are still games like that I don't like. Like Metroid or Final Fantasy, which give you a large and open world, and yet tell you nothing about where to go. Figuring it out on your own might make you feel super accomplished, but I'd like to at least not get lost all the time. And just like that, there are other games that I love a bunch even though the whole thing is just a straight line. Like Sonic Generations, it has wonderful gameplay and graphics that pull you back in to it, even though it is short and pretty much has no story. So, what about you?

I'm kinda in the middle of things. I love going out there and figuring out my own path of doing things, makes me feel I have freedom. Really puts me in a good mood for adventuring and travelling. Something I don't get from being bound to a rail just observing the scenery as I go.
At the same time, I love linear paths so I have some guidance that I'm heading towards the end of the game. I get the feeling I'm actually working to the end and finishing this. I don't feel so lost or side tracked.

I think it's more I prefer Non-linear in a game I want to last a long time and spend many days working to complete, where as if it's a game where I want to know how the story is, I prefer a Linear so I could complete the game sooner.
I can think of many examples, but that's another post.

It really depends on the type of game to me.
For example: If a game labels itself as "Adventure" then I would expect to have an open world to explore with different ways to get one thing done, a.k.a. non-linear gameplay. A good example of this would be Final Fantasy games.
However, if a game is like Bastion, where you go to one level to complete and you go back to the main hub after each level, then I would prefer it to be straightforward so I don't feel like I need to go back down each path to see if there are any treasures that I missed; I would see this as padding for the game. Another good example where this applies would be the Crash Bandicoot games.