Wow…I have been playing them for about 32 years, since I was 6 years old when the first Atari came out…and before that it was pinball machines with me up on a stool, lol.
There aren’t any that you must play, really. It all depends what you like and what your interests are. If you like strategy, or maybe first person shooter games, or the idea of building your own world…those games are out there.
I would suggest, if you have a laptop or computer, that you get a Steam account. They have tons of games and a ton of free games, including PS4 and XBOX games for PC, all in one place for you to check out. Create an Account
These are also categorized, so if you are looking for a strategy game, you search under strategy, and so on.
Maybe you like sports games? Or science fiction controlling your own fleet of intergalactic battle cruisers is something that suits you.
Maybe slaying dragons or zombies is more your style.
One I am currently playing is Robocraft. It is free, and basically you design and equip your own tank or flying vehicle and go into battle with other players online…design, build, battle. It’s pretty fun.
I really like MMORPGs…massive multiplayer online role playing games as well. One that I have been playing for about 13 years is Runescape. It isnt on Steam, but you can find it at http://www.runescape.com
Really though there are so many out there you just have to try some out that might interest you. Or if you already have some friends that play a certain game you can join them. That way they can give you tips and ideas about how to play the game and it can save some time in learning the layout of the game and learning how to play it.
Good luck! Let me know if you have any other questions.