Quick Answer: Dice games exist in virtually every culture worldwide. Notable examples: Perudo (South America), Cho-Han Bakuchi (Japan), Sic Bo (China/Southeast Asia), and Shut the Box (Northern Europe). All share the core mechanism of random dice outcomes combined with strategy or betting.
Asia: Sic Bo and Cho-Han
Sic Bo (meaning "precious dice") is a classic Chinese game using three dice. Players bet on various combinations of the three dice results. The game is popular throughout East and Southeast Asia and is found in casinos worldwide. Cho-Han Bakuchi is a traditional Japanese game where a dealer rolls two dice under a cup. Players bet on whether the sum is even (cho) or odd (han) — a binary bet that creates an authentic 50/50 gamble (the dealer's slight edge comes from structuring bets).
South America: Perudo (Dudo)
Perudo (also called Dudo, meaning "I doubt") originated in the Inca Empire and is the national game of Peru. Players each have five dice hidden under a cup. Players bid on how many dice of a given value exist across all players' dice combined. Players either raise the bid or challenge ("dudo"). The loser of a challenge loses a die — the last player with dice wins.
Europe: Shut the Box and Mia
Shut the Box is a classic game from Northern Europe — players roll two dice and flip down numbered wooden tiles in any combination matching the roll total. The goal is to flip all tiles (9 combinations of 1-9). It began as a pub game in Normandy and spread throughout Europe. Mia (or Mäxchen) is a German bluffing dice game — a simpler relative of Perudo using just two dice.
India: Pachisi and Chaupar
Pachisi (ancestor of Ludo and Parcheesi) used cowrie shells rather than dice for randomization, but its direct descendant Chaupar used long dice (cowrie-like oblong pieces) with four narrow sides. These games influenced virtually all the "race-around-the-board" games of the modern world.