The first game I will post a link for is Enter the Gungeon. It's a top-down, pixel-based dungeon crawling game, where your player is tasked with entering the mysterious "Gungeon" to find a gun that can kill the past, rumored to be found in the sixth floor, or chamber, of the gungeon. The game is a bullet hell style game, but also with lots of loot based exploring, and its absolutely full of puns. Every boss, found at the end of each Chamber, has a gun-based pun for its name, from the Beholster, a Beholder loaded with tons of guns, to the Gatling Gull, a muscly seagull wielding a minigun, to the Ammoconda, a giant Anaconda that, you guessed it, shoots a ton of bullets at you.
http://dodgeroll.com/gungeon/
Another game I enjoy is the recent team-based 6v6 FPS, Overwatch. overwatch is a lot of fun because you get to play cooperatively with 6 people you may or may not know, and work together to reach a common goal of escorting a payload or capturing an objective. The way different characters' skills and abilities is interesting, and is built entirely around teamwork for a common goal. There is also a deep backstory for every character, how they relate to each other, and the futuristic world they exist in, while almost all of this is found outside the game, in cinematic shorts, comics, and other extra-gameplay sources. The game itself is actually considered non-canon as far as the story goes. Its a lot of fun and I love spending hours on end pushing payloads and holding objectives with 5 other complete strangers.
https://playoverwatch.com/en-us/game/
