It should go without saying this is my subjective opinion based on what I have played in 2015 (not necessarily released in 2015), so don't go saying "you're wrong!", because I can't be wrong about what entertained me. Take that mythical reader! Oh, and since I'm coming up with these on the spot, they are in no particular order.
Metal Gear Solid V: The Phantom Pain
I can say hands down that this is my game of the year. It just did everything right in terms of gameplay and story (despite the missing mission 51). The number of hours I've poured into it eclipses even minecraft at this point (at least for this year). It is a testament to Kojima's masterful storytelling that he was able to evoke real emotional responses to characters in this game. You form a bond with your soldiers on Mother Base and with your support buddies. I'd say how, but that'd be spoilers, you really must see for yourself... and experience the guilt (mission 43) and grief (mission 45) that comes with it.
Metal Gear Rising: Revengeance
Back at the beginning of the year I was totally obsessed with this game, enjoying its gameplay and music. It was rather grindy, but as I said before, that music was motivation to keep trying.
Minecraft Modded 1.7.10
This year I made three custom modpacks. One I created for playing with my kids at home, and the other two were the third and fourth versions of Axpack, my single player packs. Also note that I did very little map making during this year, and that was strangely refreshing... at least in terms of not being drained by the experience.
Saints Row IV/Gat Out of Hell
This was one I played through repeatedly and to completion each time. The gameplay and story were that enjoyable and was never boring or felt repetitive. Running and jumping/flying through the city was tons of fun.
I had not finished a Tomb Raider game since the original. This was a good game to come back to. The jumping, hoisting, and shooting was varied with not too frustrating puzzles. I liked the experience and look forward to playing the recently released one.
Shadow of Mordor
Lord of the Rings with the Batman: Arkham battle system. Though the PS3 version had some pretty maddening load times between the menus and action (1-5 minutes... I kid you not!) the gameplay was great and the story was a decent one... not remarkable, but it seemed to fit into the LotR lore fairly well. The nemesis system is brilliant, and really motivated me to track down the orc scum who killed me and end them before they got too powerful. I have purchased it (but not yet installed) during a Steam sale, so I plan on giving it another shot (when I have 40 fricken GB free) and am confident my PC can play it better.
This game has been my recent conquest. A great hack-and-slash, action RPG with epic battles like Shadow of the Colossus. Yes, you can climb big foes and stab them in the head... awesome!
Two Worlds 2
I haven't invested as much time in this one as I perhaps would like. See... it doesn't control well which makes the battles awkward. It looks good and seems like an interesting world. When I get the time to invest in it, I think it'll be enjoyable.
It's one I play in spurts, but I love the combat, the mood and feel of the Shadowrun world.Choices have consequences and sometimes you just have to live with them... it's not always viable to just load up an old save. The first one was very well done and I expect the third, Hong Kong, will be as well.
Choice of Robots
A text adventure in which you are a robot developer, and make decisions about how to raise your personal robot and your life pursuits. I've played through to several endings, including:
a) My military robot killed me when I wouldn't join its insurrection against humans.
b) My robot was brow beaten into obedience and I had a happy romance ending.
c) Another military robot who obeyed better, but I decided to take over the world... of course!
d) Focused on making hippy-dippy medical robots and my robot fell in love with me.
e) A militant capitalist, I did whatever it took to get filthy-stinking rich. Did so, and had to develop a robot body when my meat one pooped out.
...and yet there are still so many more possibilities!
Back to the Future
The first Telltale adventure game I've tried, and it is very well done indeed! The voices are spot on, even for those who didn't reprise their roles. I love the series and this does it justice.