I feel like the Clue and Monopoly suggestions are a joke, but maybe not.
Board games have evolved at faster/better pace than tech the last 20 years. Think on that. If you play Clue or Monopoly or Yahtzee then you must also get your milk in a glass bottle on your stoop.
Easy to learn, 4-6p games that play in 75 mins or less:
Mysterium (an infinitely better version of Clue) - interactive, fun
Dominion - deckbuilding, fast turns
Hand to Hand Wombat - dexterity / party
Paris Connection - trains, fast actions, easy to teach, strategy
Medium - party, interactive
Pictomania (infinitely better than pictionary) - interactive, party, drawing
Power Grid - strategy, fast turns (usually), can be boring if you fall behind
Alhambra - strategy, tile laying, fast turns
Just One - party, word, trivia-ish sorta
Stella - party, imagination, simultaneous action
Happy Pigs - strategy, action selection, fast turns
Red Rising - hand management, mult-track scoring, easy to teach
Tapestry - strategy, heaviest game on list (but not super heavy), unique factions
Metro X - flip and write, fast, easy to teach, simultaneous action
Welcome To... - flip and write, new strategy each playthrough, simultaneous action
Time's Up Title Recall - party, charades, password mashup, fantastic
One Night Werwolf - any of the Bezier werewolf games, uses an app, best with 6-8, party
Pitch Car - dexterity
Diamant / Incan Gold - push your luck, simultaneous action
For Sale - bid/buy/auction, fast, easy to teach
If you have a preference on party, strategy, trivia, artsy, drawing, tile laying, card based, etc that would help narrow it down. We play 6 almost exclusively. There are literally hundreds of excellent games in each category.