RTS
Supreme Commander Forged Alliance, and SupCom 2
SC2 is different, but undeservedly panned imo when compared to Forged Alliance—if SC2 had a different name many would think it quite good.
SC series is regarded as the successor to Total Annihilation, one of the classics of the RTS golden age. It as that same 'everything is huge, build thousands' vibe, and one key UI element I'm so disappointed never took off—support for a second monitor.
Command & Conquer Generals Zero Hour
My fav C&C and most-wished-for remaster, GZH still stands up each year I dip into it. While I love most of the other C&Cs, I wouldn't recommend them to a new RTS player today.
TBS
Civilization 4 and 5
Anyone struggling with an addiction problem, I recommend finding Civ players who still have a job and a marriage—truly they have found the answer to life, the universe…
I still play both each year, and they definitely hold up. The epic scale, epic sound tracks, epic gameplay, epic game length… The degree of choice is what makes them timeless for me, rather than just pinnacles in their decade.
9 difficulty levels
World map, continents map, islands map, mountains map, lakes map…
Different map every restart
Play against 1 or 21, choose your opponents
Always war, never war, maybe war
Start in 4,000BC or 1,500AD or…
Win by military, science, culture, diplomacy, religion
FPS
Crysis and Crysis Warhead
The only old shooters I definitely half-replay at least once a year. Made by the same devs who made the original Far Cry, it's another seminal work in the dev of the open-world sub-genre I love.
CW is a standalone expansion. I only play the first half of each, since the intro of aliens at halfway ruins it for me, same as the trigens ruined the second half of Far Cry.
Subject of the long-running 'can it run Crysis' PC meme, it still looks beautiful today. Gameplay is more linear than Far Cry 3+ and the world isn't as open, but it has the open world 'feel'. Highlight is the nanosuit, which gives you short-term superpowers—speed, strength, armor, and invisibility.
Just Cause 2
See various others' posts above—it's just fun, still is today
Half Life 2
There are some great scenes in HL2—Ravenholm, the canal, the bridge—which I can still picture clearly well over a decade after playing. I dipped in 2-3 years ago and gameplay & presentation hold up well, but it's not my kind of shooter anymore, too closed & linear.
Far Cry 2
My least favorite of the series, but many people's favorite. I tried it again a couple of years ago, and it holds up just fine—if the gameplay wasn't so annoying for me, it would be an annual revisit.
Set in Africa, has great fire—the burning kind—mechanic, and lots of realism like getting sick and deteriorating weapons. A definite challenge.
Puzzle
Portal
Often classed as a shooter, Portal is much more a puzzle game imo. Simple premse: shoot a hole in a wall—or floor or ceiling—then another hole in a different location, walk into one brings you out the other. Very inventive puzzles, and of course all the time being taunted by the hilariously sarcastic GLaDOS AI. Uniquely brilliant.
World Of Goo
Fancy plopping blobs of goo around the place? Thought so, who doesn't? Use the sticky guys to build various structures—often wobbly bridges—to overcome environmental obstacles like cliffs & chasms. Uniquely brilliant.
SpaceChem
From the guy who's game InfiniMiner inspired Minecraft, this is an assembly and manipulation game—so likely to appeal to engineers, coders etc. If that's your bent, SpaceChem is a superb example of the genre.
Casual
Royal Envoy
What I love most about replaying RE and the 3 later follow-ons is that I still find a new strategy for some levels. Definitely my #1 casual game series from the hundreds I own.
You build and/or repair structures—mainly houses, also sawmills, markets, banks etc—to achieve the level's goals. Each level is one screen only, and it can get quite clicky at times if you're trying to get a 3 stars score.
The first one is probably the hardest of the series, but they're all superbly designed timeless games. This is a rare occasion where I recommend the dearer Collector's Edition, which has ~50% extra levels. Of course, try the 1-hour demo first!