Whats your hardware?

Popular Online games are probably Dota 2, CS:GO and Team Fortress 2. Theres a Rust GOL server as well.
There are tons of good singleplayer games also. Good story games like SOMA, State of Mind and Observer or Firewatch.

Best just check the steam store/GoG store and filter with Linux support and check for the ones you like :)

Linux is now a way too diverse platform for gaming, in the same scale to windows, to just give a list of popular games. It is mostly popular PC games on steam with Linux restriction.

https://store.steampowered.com/search/?category1=998&os=linux

This alone is way too many games.

To brake it a bit.

Almost all Valve games
like: Portal2

Games ported by Feral interactive
https://www.feralinteractive.com/en/linux-games/
like: DiRT Rally

Most new games from Paradox Interactive,
like: Stellaris

Games from smaller companies (or indy) or ported from smaller companies (or indy)
like: Rocket League

I think Linux is especially strong on adventures and strategy (not only from Paradox)

Also, most "windows only" games do run fine with Proton (wine based compatibility layer for steam)

Other places to look:

https://www.gog.com/games?system=lin_mint,lin_ubuntu&sort=popularity&page=1

https://itch.io/games/platform-linux

https://www.humblebundle.com/store/search?sort=bestselling&platform=linux

Free games
like: The Battle for Wesnoth

Browser games
like: https://www.kongregate.com/

Other means
like: dosbox, scummvm, wine

Also, so far in my opinion at least the best place for news about gaming on linux is (by far)
www.gamingonlinux.com :P

Best is relative, however these are my favorites :

Metroidvania: Hollow Knight. It's beautiful, has a nice but subtle lore, long playtime period, and satisfying control. Not to mention it's cheap and the developer is great.

Roguevania: Dead Cells. It's a fast paced game with beautiful graphic. The world is generated with several constraint, so every playthrough is different but still similar, so you can learn as you die. The downside is there are almost no lore to learn.

Strategy: All Paradox and Firaxis games. My favorite is Crusader King II, where you play as a noble in middle ages. In this game, your goal is basically to expand your dynasty and expand your realm. To do this, you have to do many thing, e.g. managing your vassals, inviting talented person to your court, marrying your heir with genius or strong person, fabricating claim for another counties, etc. You can also do bizzare things like killing your imbecile son to prevent him become your heir, seducing all girls in your court to spread your seeds, or if you play as zoroastrian, you will need to marry your close family (incest) to retain the "blood purity" of your dynasty. At the end, you will realize that to destroy a great dynasty, you only need one crazy idiot to become a king.

Puzzles: All Zachtronics and Tomorrow Corporation game. All of them are original and great in their own way.

If this is your first time using Linux, you might want to check some open source game to see what we old Linux users used to play before Steam comes. In fact, I still play some of them to this day. My favorites are Battle of Wesnoth, Freeciv, OpenTTD, Endless Sky and 0 A.D.

Actually , what genres do you like ?
What do you like to play solo and what do you like to play online ?

Here we go..

FPS Single Player:
Metro Last Light Redux
Metro 2033 Redux
Bioshock Infinite
Dying Light
Superhot
Half Life 2
Borderlands 2
Doom (not native, but works out of the box when you enable Steam Play in your Steam account)

FPS Multi Player
Day of Infamy
Insurgency
Arma 3
Team Fortress 2
CS:GO

RPG
Divinity Original Sin: Enhanced Edition
Deux Ex: Mankind Divided
Pillars of Eternity I, II
Tyrrany
Star Wars: Knights of the Old Republic II
Witcher 2
Planescape: Torment: Enhanced Edition
Hand of Fate 2
West of Loathing
Undertale
Transistor
Mount and Blade: Warband

Action Adventure
Tomb Rider, Rise of the Tomb Rider
Mad Max
Hitman 2016
Saints Row IV

...

I tried to list all my favorites + most popular ones in each genre, but I give up, it's just too many. You really need to tell us what kind of games you like.

Nethack!

I'd also recommend that if you are a gaming newbie, on Linux at least, then there are plenty of high-quality games which were released within the last few years and are regularly for sale at very good discount. I've built up a massive collection of games myself this way, and if you've not paid much for it and you don't really really like it then you've not wasted much getting it in the first place.

Some of my own favourite games, which I have spent loads of time playing on Linux include:

FTL: Faster Than Light
Slay The Spire
RUST
7 Days To Die
Dying Light: Enhanced Edition
Torchlight II
Shadow Warrior (2013)
Tomb Raider (2013)
Mad Max
Rise of the Tomb Raider
Dungeon Warfare
Serious Sam 3: BFE
Crypt of the Necrodancer
Kingdom Rush
Kingdom Rush: Frontiers
Sky Force: Anniversary
Sky Force: Reloaded
Ziggurat
Xonotic (free)

Looks like a hit and run.

Quoting: damarrinLooks like a hit and run.

Guessing you are saying that because the original poster hasn't responded. Well, it's not a big deal, we *all* benefit from reading comments like the ones above, not just the forum poster.

Quoting: g000h

Quoting: damarrinLooks like a hit and run.

Guessing you are saying that because the original poster hasn't responded. Well, it's not a big deal, we *all* benefit from reading comments like the ones above, not just the forum poster.

Indeed. For example, thanks to your post I remembered that 7 Days to Die is a thing. I completely forgot to add it to my wishlist.

Also, how good is Crypt of the Necrodancer? I was eyeing it a lot in the past, because I love when games have music in sync with gameplay (like Doom 2016, Distance, Pyre). However, the gameplay of Necrodancer didn't seem like my kind of thing so I opted to skip it.