So You Think You Know Baseball?

From retrosheet.org

What is a courtesy runner?
What is a mid-play runner?
What is a courtesy fielder?
When was the last time each one occurred in a major league game?

Courtesy Runners
Until 1950, a courtesy runner was allowed for a player if that player had been injured and at the moment couldn’t continue. The original player then stayed in the game defensively in the next inning. Most often the courtesy runner was already in the lineup.

Last time it occurred
7/2/1949 (Browns at Indians) - In the bottom of the ninth inning, Ray Boone was hit on the arm by a pitch from Karl Drews. Jim Hegan, already in the lineup catching, ran for Boone and scored. Since this inning was the end of the game, the players do not return to their defensive positions.

Mid-Play Runners
When a player who was entitled to advance was physically unable to do so. A pinch runner is allowed to enter the game and complete the play. These are not courtesy runners because the replaced player did not later come back into the game. The relevant rule is 5.10(c)(1) which allows for the replacement of an injured runner in a dead ball situation before play resumes.

Last time it occurred
9/14/2005 (Red Sox at Blue Jays) - In the top of the 5th, Gabe Kapler was on first when Tony Graffanino hit a deep fly ball near the line in left that Kapler thought might be in play, so he started running hard. As he rounded second base, he ruptured his left Achilles tendon and sprawled on to ground. The ball went over the fence for a homer, but Graffanino wisely stopped at second base while Kapler was attended to. After many minutes, Kapler was loaded onto a cart and taken off the field. Alejandro Machado, appearing in his 4th Major League game, entered as a pinch-runner and scored his first Major League run in front of Graffanino.

Courtesy Fielder
Due to an injury, a fielder cannot continue and there is not a replacement available

Last time it occurred
8/10/1952 (Cubs at Pirates, game 2) - In the top of the ninth of the second game of a twin bill, Pirates catcher Clyde McCullough was injured and could not continue. The Pirates two other catchers, Eddie Fitzgerald and Joe Garagiola, had already been used in the game as pinch hitters. With the approval of Cubs manager Phil Cavarretta, Fitzgerald was allowed to replace McCullough. The Cubs won the game 4-3. Under the playing rules in effect since the 1950 season, that was an illegal substitution that the umpires should not have allowed.

From retrosheet.org