Catan is the game that introduced an entire generation to modern hobby gaming. Build settlements and cities on a randomly assembled hex board, gather resources when their numbers are rolled, and trade aggressively with the table.
The trade dynamic is what separates Catan from every other Eurogame. Every roll that doesn't produce for you is a chance to negotiate, persuade, and pressure your neighbours. Reading the table is half the skill, math the other half.
Thirty years on, still the cleanest answer to "what should I play with my non-gamer friends?"