Just generally I enjoy quiet moments. This goes for TV too. Most people want to get to the big actiony parts but I enjoy the parts like Drake wandering in the dessert and roaming around Skyrim's forests just as much as falling from a plane and killing dragons. That's part of the reason why I love Journey so much. Having quiet moments gives the louder ones more significance. If you don't juxtaposition those big moments you get every COD since 4 story wise. A rollar coaster ride in which no moment seems cool because the constant explosions just get boring (BF does this too). It's why "All Ghillied Up" is still my favorite COD level of all time.

By branching storylines, I mean a decision you make halfway through the game that will effect the outcome later in the game. An alternate story like in some of the Resident Evil games can be really good if handled well.

When I complain about branching storylines, I'm mainly referring to Final Fantasy XIII-2 and Persona 4: Golden. The alternate endings and branching paths kinda spoiled the overall story for both games, it's a real shame.

Yes! I loved Double-Dash's mechanics! But a lot of people hated it for some reason

For me I would say the main one is the ocean in WW - it was a fresh and brilliant adventure!

But here's a more recent one: New Super Mario Bros. U.
In NSMBU, there's a sense of wonder again, of exploration and discovery. New Super Mario Bros. U fully recaptures the spark of Mario's 2D heyday, something the wii and 3ds titles fell short on. But people point it out as a game that is just more of the same old 2d mario and 'Ain't nobody got time for that!'. I think that the mere existence of NSMBW and NSMB2 (both rather mediocre titles) are what is holding people back from seeing the true masterpiece that is NSMBU (I absolutely love that game for what it is).

Change the art style, music, and name and this game would be hailed as a classic masterpiece.

Junction system in FF8. I much preferred openness, customizablity, and versatility of this system to the standard grindy level up systems in other FF games.

Grinding for experience. Linear story. Turn-based gameplay. Text-based dialogue.
Basically, everything people hate about old-fashioned JRPGs.

The buggy part was where I realized how much I enjoy this game. It was amazing before I just haven't realized how amazing, the Buggy part made the game feel like I was actually there. I spend hours on the roads just exploring all houses looking for ammo. Or "cleaning" an area by throwing everything that was movable from a cliff with the gravity gun. 

I like Nintendo games which a lot of people on internet seem to hate.

I like dialogues and bond between characters ( thats why TLoU, Beyond and Bioshock Infinite are so amazing games for me ) Moreover I like deep story, deep characters etc.

I like the more cheerful characters in games, like Rikku, Irvine, Selphie, Vanille, Snow, Wakka, etc... These are characters people tend to hate, and instead like the more dark depressed characters like Lulu, Kain and such, or steroid pumped characters from FPS/action type games who have some sort of personal mental dilemma.