I look for a character that I can relate to. I always have more fun when I feel an attachment to a character due to their past, the way they express themselves, the choices they make, the way they carry themselves, etc.
I also look for options. I like to be able to make choices in the game, whether it be which path to take, my appearance, the people I befriend, the places I go. I like an open world, where I'm not being pushed along from level to level.
I also like a large and beautifully designed map. Take Legend of Zelda: Twilight Princess for example. The world is so vast in that game, I often forget that some areas even exist. Finding them again later is such a pleasant feeling, it's like rediscovering it all over again.
So, When you've played through all of your games and you feel like it's time for something new, what do you look for?
And for those of you who are into FPS, what do you look for in those? I'm quite curious what makes a good first-person shooter in your eyes.