Compile (later Compile Heart) is most famous for the Puyo Puyo series (originally Puyo Puyo 1991), a competitive falling-block puzzle franchise that became a global phenomenon (localized as Dr. Robotnik's Mean Bean Machine, Kirby's Avalanche, Puyo Pop).
They also developed the acclaimed Zanac (vertical shooter), Aleste / MUSHA (shooters), and Madou Monogatari (RPG/dungeon crawler, precursor to Puyo characters). But Puyo Puyo remains their defining, longest-running IP.