1. N++ - This game is amazing for both single- and multiplayer with thousands of well-designed levels, and multiple game modes. I think some people may have overlooked this game, since the name and look were so similar to the previous games in the series, N and N+. But there's so much new under the hood and so much new content that people should seriously check it out. (PS4 only right now, I believe)
2. Mushroom 11 - With so many new games coming out each year, it's hard to invent a truly new game mechanic. In Mushroom 11, there is a blob that has the property of always trying to maintain a fixed mass. Your goal is to guide the blob through a post-apocalyptic environment by shaving parts off of the blob. If you shave parts off of the back, more mass grows on the front. If you do it quickly enough, it's sort of like pushing the amorphous blob through the world. Because of its amorphous nature, there are a lot of physics puzzle challenges that emerge. (PC only)
3. Human Resource Machine - HRM basically models how a CPU works, but it's all set up in a very Kyle Gabler (World of Goo/Little Inferno) style. The beginning puzzles are relatively easy - even to achieve the bonus goals, but by the end, it gets pretty complicated.
4. Subterfuge - RTSs like Starcraft tend to be about managing lots of resources and responding to events efficiently and quickly. In many ways, they're more akin to a frantic race than planned out strategy. Subterfuge, by contrast, is very slow by design. It's multiplayer-only, and each playthrough can last a couple weeks. You manage a few different cities which produce subs, and you can send those subs to other cities to take them over. However, they take hours to get there, so there is plenty of time for opponents to respond. As a result, the real gameplay takes place off-screen, with people conspiring to gang up on other players.
5. Beginner's Guide - A very introspective and thought provoking game. It's hard to talk too much about it without spoiling it, but I will say that it's probably best to play through the entire thing in one sitting (which will take you about 2 hours). The issues the game raises are relevant to many other walks of life. It's not a "fun" game in the sense that most others on this list are. Instead, it's more of an experience to contemplate later.
6. Her Story - Fascinating way to tell a story in a non-linear way. You use a '90s style computer interface to access police videos of a woman being questioned. By typing in different search terms, you can find more videos. The more you search and pick up new names and places to hear about, the more of the story you uncover.