Paul Morphy vs. Duke Karl of Brunswick & Count Isouard
Why It's Famous
Played during a night at the Paris Opera, with the American Paul Morphy facing two aristocratic amateurs playing together in consultation (a Duke and a Count, jointly deciding Black's moves), this remains the single most-taught model game in chess instruction for rapid, principled development.
Morphy develops every piece with purpose, refuses to waste time chasing pawns, and finishes with a stunning queen sacrifice (16.Qb8+!!) that forces the king's own knight to block, clearing the way for 17.Rd8#.
It's frequently the very first "full famous game" shown to beginners, precisely because every single Morphy move follows classical opening principles (development, center control, king safety) that are still taught exactly the same way today.