I'd prefer if it still had a main story that you can follow, as long as they gave you enough freedom to sidetrack and do other things

sort of like Fantasy Life.

I get your point, but I feel like that's not really the MAIN story, more like an environmental feel/motifs the story gives off that it really starts to kick in once sidequests are partaken, but it's not the main story.  And eh, I hear it's not really a pressure to finish the objectives because you have songs that slow down time/restarts the 3 day cycle.

It matters to me, yes. That said, I'm more willing to forgive a mediocre main plot in an open world game full of tons of other fun/interesting things to do than I would be in any other type of game. Elder Scrolls and Fallout games are great examples of this.

But if you get the main plot right on top of having a massive world full distractions....that's when you have something really special.

You have a point, remind me of Minecraft.  Don't really know if there's a story to it, but the fun my sister is having with that game is creating and exploring. 

I usually don't know what the story is about in most open world games because of the exploring and side quests.

Not necessarily. If the game allows for a certain level of roleplaying and has a decent amount of side-quests it's very much possible to enjoy the game without giving a damn about the main plot. It all depends on the game and how you choose to play it.

The exploring and the side content are maybe more important in open world games. In fact, that's the reason why open world games exist, as I see it. If you only want to focus in story, make a linear game, and that's it. I usually love games with a linear main story and lots of side quests and exploring to do. I can forgive that the story of the game is bad, but, I can't forgive if the world is boring and the side content unispiring.

Hmm.

Hmmmm.

I want to say 'yes' but, quite honestly, I often end up super powerful and grow bored of the game without ever completing the main quest. I never beat Skyrim, despite starting over twice and being a virtual god on earth each time. I never completed Far Cry 3 or 4, despite taking all the bases and towers and unlocking all the weapons and doing pretty much everything I wanted to accomplish. I did beat Fallout: New Vegas, but not until like my third character.

However, I think having events that keep pulling you forward while opening up new content are important. There are times when I fire up FC4 where I just want to go out and have fun and other times where I want to work toward a goal.

I'm confused now.  Okay, the main story of Majora's Mask is that you must fine the 4 guardians to help repel the moon that is soon to collide with the land of Termina and ultimately kill the people.  The game starts you off in storyline as a Deku shrub.  You aren't able to transform into Link until the story gets to the point where you can.  Yeah, its envirmental feel/motif, but the game is strongly based on story.  What made Majora's mask so enduring to players were the cause and effect of what happens to the people of Termina because of what's happening with the main story.  As the 3 days nears its end, the game and its enviroment also changes because of the story.  By the third day, you can feel a sense of urgency, the land actually trembles.  The story makes the game, the exploring stuff is good, but the story makes it. 

Watch the game theory episode of majora's mask and see why it was so heart wretching to have little malon's sister go to sleep.

Depends on the game, tbh. Basically what Jizz said.