Under current BWF laws, a badminton game normally requires 21 points to win.
Badminton uses rally scoring, so the side winning each rally scores a point, regardless of which side served. A game is normally won by the first side to reach 21 points, but a two-point lead is required once both sides reach 20. This means a game can continue beyond 21–20.
The extended game has a firm ceiling: if the score reaches 29–29, the next rally decides the game at 30–29. A standard match is generally the best of three games, so the first side to win two games wins the match.
The 21-point format replaced the older service-over scoring system in international badminton during the 2000s. Under the older system, only the serving side could score, and games were commonly played to 15 points in most events. That historical difference is why older references may give a different answer.