Go. It's nobody knows how many thousands of years old, it's easy as pie and difficult like crazy. The game can't end in a draw. It's easy to balance strong and weak players so they can compete with full effort. The equipment is trivial to make with common, cheap household items. Computers got competitive against humans just a couple of years ago (compare to chess where they beat humans in 1997 and ever since).

Betrayal at House on the Hill

Great board game for 3+ people. Best with a full crew. You and your mates explore a mansion. As you explore a new room you place a tile and something can happen.

It's meant to have a lot of replayability as each time you play there's a booklet full of potential end games that you can trigger. Such as the mansion is burning down and you need to escape.

My absolute favourite is Spirit Island. A co-op game where you work together defending your island and kicking out explorers and settlers. Expanding your presence and getting new powers along the way. Every game with new combinations.

When we got the game we played this more than once every week for over a year. With each game taking 1-3hours with our playstyle. Sometimes longer with four players (but that's partly because of not actively playing the game then). We play less now only because of moving with the renovation taking too much time.

Wingspan is really great plus it has stunning visuals too!

Ticket to Ride. Building out your rail network is so satisfying.

Clue.

Mancala, if that counts.

Power Grid

Single favourite is hard to pick.

Casual: I agree, Ludo is GOAT.

Invested: Catan..... Maybe Scrabble

Dumb fun: Mad magazine game

Solo: Mage Knight

2 player: Star Trek Fleet Captains

4 player: Shadows of Brimstone

Stupid-fun dice chucker for 4 or 5: Project Elite

Call to Adventure, Wingspan/Wyrmspan, most of the Tiny Epic series, Coup are all solid contenders.

I like the Red Raven games but I don't really look forward to playing them because of all the set up and tear down lol, I would love them as digital products with automation.

That is easy to answer for me.

Mansion of madness

I have played so many rounds with so many different people. The game is complex enough that each round is different. But easy enough to geht people to start with. Easy to play hard to master.

The digital game master via APP is great. I had so many games in which the last player actions decided the game. After some hours of game time. Your actions feel so impactful.

The ones I usually carry around to introduce people to good boardgames are: Hive Portable it can get as complicated as chess, but is really easy to pick up for kids and adults. Carcassonne chill and you can pick and choose expansions Forbidden Island (and its family) it's a fun cooperative game that's easy for kids to pick up.

My wife and I really like Agricola. It's a farming-based people-placing game created in Germany for 2-4 players (with the base game), but there is an expansion for 5-6 players. We do play with a decent amount of house rules, though.

Heroquest.

so many good options on here already so I'll add one that's a little more of a dedicated game:

Arkham lcg.

you create a deck that represents the character you will play in a series of approximately eight games where you cooperatively work through Lovecraftian mysteries loaded with interesting stories lore and twists.

has almost a tabletop RPG feel to it if it was converted to a card game, absolutely love it.

Right now, it is Azul.

I really enjoy Root, but it can end up taking a little while to get through.

Labyrinth - if you've never played it, all the players are moving around a maze collecting items on cards they draw from a deck. Whoever collects them all first wins. You can move as far as you want each turn, but the catch is you first change the maze (the whole board being made of movable tiles), then move your totem. It encouraged complicated spacial reasoning and leaves room for sabotage of other players. Any number of players can play; you can even solitaire it if you want.

Cameroon. It's like a mix of air hockey and pool.

I wish I had an actual board still... I only have it via 52 Clubhouse Games on switch. I find it much more fun when you're actually flicking the pieces with your finger.

Backgammon

Dixit is one of my favorites, and very fun to play with a group of people you know well. Sort of like Pictionary with cards instead of drawing, but you try to only get one person to guess correctly.

Small World was my introduction into alternative board games, and still one of my favorites to help introduce new board games to people who have only played Monopoly.

I like Root, its like an asymmetric Risk.

I treat Chinese checkers with the same reverence and over-seriousness that chess players have towards chess. I'm not especially good at it, but I really enjoy it.

Unfathomable hands down.

It requires 3-6 people for well over two hours (longest was around 5h).

Constant attacks from the sea creatures trying to destroy your ship. With traitors.

But it's so engaging and fun. There is enough depth for replayability, lots of variation, there is always something happening, and players interact a lot, so there aren't boring parts just watching someone go off with their turn.

There was recently an expansion, adding lots of variety and more depth.

Almost everyone who played once wanted to try it again. If you can find people who have the time, they will not walk away until it's over. And will think about how to play differently the next time.

Cosmic Encounter

No two games are ever the same. So are the attempts to lure people in and out of encounters, and the following betrayels. Great fun.

Mysterium among others already mentioned. Very similar core mechanic to dixit, but co-op and some what longer/more expansive.

Outsmarted. Technically a board game but with an app.

It’s actually not the gimmick I thought it would be! Cast that bad boy to the tv and you’ve got a game show in the family room!

I love the second edition of Merchant of Venus.

Pictionary

I’ve had the most fun with Burgle Bros