Are there any sports other than American football that have a coach's challenge? I would like to know if there is a sport other than American football that have a coach's challenge.
As of 2014, Major League Baseball adopted its current replay system, in which each manager can challenge a call one time per game, and gets a second one if the first call that they challenged is overturned.
The official rules for challenges can be found at http://m.mlb.com/official_rules/replay_review.
It's not a coach's challenge per se, but cricket has the concept of player reviews, where either the batsman or the captain of the fielding side can request a review of an umpires decision.
The National Hockey League also has a coach's challenge, as of the 2015-2016 season (official announcement). Coaches have a single challenge, which can be used to review a scoring play. If the challenge is unsuccessful, the team loses its timeout. If successful, they retain their ability to challenge later.
In Field Hockey each team has one video umpire referral per match, it seems limited to FIH World-Level competitions though (/when facilities are in place).
As with the cricket example, it is the captain doing the actual challenge. If the challenge is succesful they keep the ability to challenge, if not they can no longer challenge in that game. As long as they make succesful challenges they can challenge again.