That's a question with a lot of variables.
I grew up with reading as my primary hobby, so I need for most games to engage my imagination to some degree. A quality plot, good storytelling, compelling characters, and interesting dialogue are all positives. I can deal with a game that has a mix of good writing/mediocre gameplay more than I can most games that have good gameplay/mediocre writing. It's the way I'm wired. If my imagination is just sitting there turning into jelly, I'll probably be bored and find something else to do.
There are some exceptions. Games with a high degree of strategic gameplay that demand your full attention are awesome. I play chess on my Vita pretty much everyday, for example, and I love games like Final Fantasy Tactics. My imagination might not be engage during the gameplay but my brain is working. I consider games like Gran Turismo to be in that same category, as racing can be very strategic and immersive.
I like RPGs and tactical RPGs such as Suikoden, Final Fantasy, Dragon Age, and Valkyria Chronicles. I like sci-fi FPS games like Fallout 3, Borderlands, Portal, and Killzone. I like Gran Turismo and AudioSurf.
I don't like shallow platformers where the story is an afterthought. Mario bores me to tears. I don't like military shooters or most TPS games.
