Choices feature more or less in some games. There are games that are truly linear offering no choices [such as the excellent Beyond Good & Evil], games that offer some choices [such as BioShock with the little sisters which affected the finale] and games that are all about choices [such as the Mass Effect trilogy].
Having choices in games means that the experience is more tailored to me and I can play it the way I want it to and I will mostly choose [ha!] a non-linear game to have the chance to make choices. To be able to shape the game how I want it without having to do things that I don’t want to. Charlie Brooker recently wrote about his experiences playing MW3 which are relevant to this:
[...] my character also grabs the guard and stabs him right in the throat. And I thought, “I’m no better than moustache man: that was an appalling thing I just did.”
I have issues with games that seemingly give players a choice without actually giving them one. Such as the Ninja Gaiden 3 demo. In the initial part of the demo the player has to fight through several soldiers in London until there is only one of them left with his hands raised. The interactive cutscene allows the player to walk up to him closer whilst he is pleading for his life, taking off his balaclava and mentioning his wife and children. The only option is to keep going closer towards him and then eventually striking him down. Eurogamer describes it pretty well in its review:
It’s an illusion of choice, of course. There is no decision to be made, no capacity for mercy. You must press X to eviscerate. There is no other way.
I quit the demo just after that.