I'm a big fan of open-ended games. Something that drops me into a world and lets me play around. I do enjoy more structured, linear game play experiences but I find the games that I put the most time into are titles like Oblivion, X3 Albion Prelude, Terraria or even something like GTA where I can roam around at my leisure.
So what do you prefer? A more linear, focused experience or something Open-ended & sandboxy?