It Takes Two - one of the rare two-player splitscreen co-op games on the market. And an amazing game as well - play it with your best friend or SO, get laughs, maybe even feels, and a super fun experience! Can also be played online, and only one player needs to buy it.
For online gaming, the We Were Here series is a finely crafted quartet of 2 player co-op puzzle games. The first installment is actually free to play on PC, so you can give a try if you enjoy the concept. Later games have much higher quality though, and so far every subsequent game has more or less doubled in length, and each one can be played twice as you can change the roles for each puzzle!