I'll talk about some of my favorite games in batches. I'll start with short games first.
Short games:
The Resistance is probably tied for my favorite. It plays 5 to 10 players, and scales quite well. Watch the Tabletop video for rules
https://www.youtube.com/watch?v=g_QRczGzXqw. This game is always a blast, and since it plays quickly, you can get several games in. The tension that builds up during the game is palpable, especially in games with more players where there are more unknowns. I always bring this game to game night, and it is a great way to close the night. One time we started playing at 9:45, and kept playing games until about 1 am sitting outside of a closed Starbucks. I recommend that at least one copy of this game should be owned by someone in a group, and provides more bang for your buck than most games. There are also expansion modules that make things more complex if the basegame gets a little too straightforward.
Skull or
Skulls and Roses is another group favorite. It plays 2 to 6 players, but I think 3 is a functional minimum. It's a bluffing and betting game. I haven't seen any good videos for it, the two I watched I can't recommend due to errors. Each player had 4 tiles, 3 roses and 1 skull. You tried to bid how many tiles you can flip over without hitting a skull, or you try to induce other players into flipping over a skull. There are more to the rules than that, but it plays at a little less than 3 minutes per player.
Coup is another short game that plays 3 to 6 players. I have two copies of the game, and we've tried large games with 7, 9, and 10 players, but it's too hard to keep track what is going on across the table usually. Seven players worked decent though. Tom Vasel does a decent overview here:
https://www.youtube.com/watch?v=9YySzHXa1mo Each player has two characters that are not revealed to other players. You can take actions based on one of the character cards you have, take one of two generic actions, or just lie and take the action of a character you don't have. Players have the opportunity to challenge other players lying about roles, and getting caught bluffing has the pretty dire consequence of losing one character. Lose a second and you are out. All the while, you are trying to gather money to assassinate or coup your opponents, causing them to lose a character. Lots of intrigue and tension.
Star Realms is a quick deck-building game that can play any even number of players, but I have only played 2 players. Players buy ships and stations that either give them economic power, attack their opponent, or heal/repair. I'll talk more about deck builders in another post (if people keep coming to this thread). I put it in the quick games, however, because it lacks the set up time a lot of deck building games have. I can whip this out and get started in less than a minute if I put it away the way I want it put away, whereas other games usually take some time to set up.
Here are some other types of games I'd be willing to talk about in future posts. Speak up if you are interested in one of them (or a particular game if you look at my bgg profile).
Co-op / co-op with traitor games
Deck Building games
Worker Placement games
Economic games
Tile placement games
Area/object control games
Space games
Role games (where your character or role dictates what you can and cannot perform)
War games
The broad topic of "Euro games"
Gateway games
Heavy games
2 player games
or, maybe just my favorite games
If I do a list, write ups will be a sentence or two tops and I would probably do 5 a day or so and knock it out relatively quickly.
There are lots of overlap in those groups