I'd love to see The Room 1 to 3 ported to Gear VR as one huge game, or at the very least The Room Three since it's at least a six hour game. The developer, Fireproof Games, has already released Omega Agent for Gear VR, so they have the necessary experience. The art assets in The Room, including music and sound effects, are amazing and would be incredibly immersive in VR. Amazing game all around, developed for mobile phones, so it could be a great fit for Gear VR.
In Cockpit View Yet Very uniquely Interesting Game
Zombie Gunship (*Awesome for gaze base lock down and touch-pad shooting) game being easy on resources(This very old game was available since iphone3 so i guess it can be very well ported with awsome quality updates to Gear VR)
Crystal Rift - Legend of Grimrock is awesome so it would be amazing to see this on Gear VR. But there hasn't been much news about a Gear VR port, other than the Twitter page says it's for the Gear VR.
Myst-like game - Puzzle solving and exploration seems like a no-brainer for VR. Land's End was pretty shallow though and the "puzzles" didn't require two brain cells to figure out.
Dead Secret 2 - Dead Secret has so far been a high-water mark for my Gear VR experiences. It would be awesome if they made a sequel.
Zelda-like game - Herobound: First Steps is awesome but lacked challenging puzzles and the enemies were all sort of similar even though they looked different, which made it a little repetitive. Also there was basically no story-line. Herobound with a few improvements would be in the Nintendo category of games. (EDIT: Just started playing Herobound: Spirit Champion and it is perfect! It is blowing me away and exactly the Zelda experience I was looking for.)