My major was game design, so I have a lot of board games.
Board games:
* Catan: 3-4 players. Get points by advancing your settlement.
* Tokyo Highway: It's like Jenga but everyone is trying to build highways over each other. 2-4 players.
* Planet: 2-4 players build their own planet by adding terrain each turn to be hospitable for different animals.
* Evolution: Sort of a deck-building game. Trying to make to most successful species. 2-6 players. It's really fun, but a little complicated for younger players.
* Ca$h n Guns: 4-8 players. Band of gangsters arguing on how to split the loot.
* We're Doomed!: 4-10 players. It's cooperative but since my friends live for the chaos it always ends in betrayal. You're trying to build a rocket to escape the planet in 15min (timed), but there usually aren't enough seats for everyone.
* Betrayal at House on the Hill: 3-6 players. This game has 2 phases. The first one is exploring the haunted house by walking through dorways to generate new rooms. The house looks different every game. The second phase is when someone betrays the group. The way this happens depends on the rooms unlocked and is also different every game.
Card games:
The amount of people who can play these is only limited by how many decks of cards you have.
* Mafia: You can play this one with a deck of cards. The rules vary by household but basic guides/rules are online. It's also called wearwolf. It's what the game Among Us is based on.
* Screw your Neighbor: fast paces, easy to learn. It's a good go-to if there are 6+ people.
* Thirty-One: The goal is to obtain a hand that totals 31 in cards of one suit, or to have a hand at the showdown whose count in one suit is higher than that of any other player.
* Hearts: Be the player with the lowest score at the end of the game.