This post is an edited version of one that also appears on my personal blog at http://storytellingdream-thief.blogspot.com.
Not every game is going to be your Heavy Rain or Alan Wake. In an attempt to save you more time so you can spend it on the things you enjoy, here is a simple check-box list you can take a look at to determine whether you're really enjoying the story you're living :
1) Do you relate to the main character?
Can you understand where the main character is coming from and, more importantly, are you interested in where they're going? If not, put the game down and walk away. You're essentially living with the Hated Ex.
2) Do you feel like you understand enough of what's going on in the story?
Do you feel like you're being drawn into a mystery, or are the character motivations clear enough to keep you engaged in the storyline? No one wants to take tea with Master Yoda, especially if he's not going to teach you to be a Jedi. Chances are, whatever you're playing ain't gonna, so move on.
3) Is it frustrating you?
Now, some games use frustration as a technique. I don't mean vague I-need-to-beat-this-level-or-get-a-better-score frustration. I mean killing you over and over, having a protagonist who never learns anything or just plain not going anywhere anytime soon. If you like that kind of thing, go ahead, but I like my stories to have a direction other than 'standing still'.
4) Do you laugh in a pitying way?
If you giggle inadvertently when the space captain says, in all seriousness, "They want war, we'll give 'em war," chances are it's either out of character, out of context, or just generally poorly chosen. Voice acting or animation may come into it, but, generally, if you're laughing at things that aren't meant to be funny, you're either watching a B-Grade horror movie or wasting your time. Proceed as appropriate.
5) Did you lose track of time?
If yes, keep going, within reason. If no, that's not a bad thing, necessarily. If you ticked off every five minutes of the intervening hours, quit it. You have better things to do with your time.
6) Are you also playing Facebook/texting/reading webcomics?
If you're multitasking, it's not gripping you. Move on.
7) Did your friend like it?
If yes, accept that you may not. Move on.
8) No, they really, really, really, really, REALLY liked it!
Is this someone you're trying to impress? If yes, cut it out. Have the guts to tell the truth. If no, why are you bothering? The nature of any form of expression, games in particular, means you will never have an identical experience to someone else. Just because my friend loves Descent doesn't mean I will, and he will still hate the Sims 3 no matter how exciting I tell him interior decorating is. We're different people. That's okay.
9) Do you feel empowered by reading/watching/playing your whatever?
If you don't feel good after your jaunt into imagination, then I would argue it wasn't worthwhile. Feeling good comes in many flavours - not just the warm 'n' fuzzies, but feeling whatever you want to feel, such as feeling sad at the end of the Lord of the Rings trilogy, or angry at the end of BioShock. If you come away from a story-based interaction feeling awful - or worse, feeling nothing - then that's a sign to spend your time elsewhere in future.
10) Did it change your life?
I mean this. Has playing this game made you rethink some aspect of your existence? Surely not all recreation needs to be for self-improvement... right? Considering you take in information from so many sources at so many times during all of your waking hours, yes, everything should be helping you determine either who you are or who you want to be. Planescape: Torment changed my life, but not in the same way as Aion did. Planescape set me on my current career path; Aion made me want to go clothes shopping, but it also opened my eyes to the worlds of design and in-game architecture in ways that I hadn't seen before. I learned from both of them, so if you're not learning, what are you doing?
11) Did you pay for it?
Is that really the only reason you're playing it? Be honest. I hate wasting money as much as the next miser, but when you look at a shelf of 100 PS2 titles you've never touched, they've gotta go. Accept it was a poor decision-making on your part, and download it from GoG.com in 10 years when you have the time to play it.
Having said all of this, there are arguments for experiences. I agree. You may just want to be someone else for a while. That's okay too. What's not okay is wasting your precious free time on writing that doesn't connect with you personally, just because you don't know any better. Now you do. Go forth and be joyful.