Robert Kevin Appier (December 6, 1967) was a right-handed pitcher for the Kansas City Royals, Oakland Athletics, New York Mets, and Anaheim Angels.
Appier had a strong rookie campaign for the Royals in 1990, going 12-8 and posting the leagues fourth-best ERA (2.76). After a 13-win campaign the next year, tied for the team best, he was the opening day starter in 1992 and posted a 15-8 record with the league's second-best ERA (2.46) for a team that only went 72-90. He had his best campaign in 1993, going 18-8, leading the league in ERA (2.56), and finishing third in the Cy Young Award balloting. In 1995, he made his only all-star team.
Despite being one of the better pitchers in baseball during this time period, his accomplishments went largely unrecognized due to playing for the perennialy terrible Royals. He signed a long-term extension before the 1997 season, but after a mediocre season he finally became fed up with the organization and demanded a trade. An off-season fall resulting in a torn labrum caused him to miss nearly the entire 1998 season instead, and he remained with the team. He was still unhappy, however, and eager to play with a contender, so he was dealt to the Athletics in the middle of the 1999 season.