From 1947 to 1958, Major League Baseball operated under the "Bonus Rule". Under the rule, if a team signed a new player to a contract worth more than $4,000, the team had to keep the player on the 25 man roster for 2 years and could not assign him to a farm club. If a team violated the rule, the player was exposed to the waiver wire. After 2 years, the team could assign the player to the minors. The rule was re-instituted in 1962, when the leagues expanded by 4 teams. It was finally repealed in 1965 when baseball instituted the draft system.
It was called the "bonus rule" because it prevented wealth teams from giving large signing bonuses to young players and then stashing them in the minors, which was the practice prior to 1947.
Players between 1947 and 1965 that went directly into the majors under this rule were called "bonus babies". You can read the Wikipedia article, which is where I got most of my information, here.
The best list I could find was at Baseball Almanac. The list is of every player who went directly into the major leagues so you have to know something about the Bonus Rule to figure out who is who. The list is not complete as 4 of the 4 Hall of Fame Bonus Babies are not on it.
Since this is a baseball card blog, let's look at some cards of Bonus Babies.
As near as I can tell from this list, Curt Simmons of the Phillies seems to be the first Bonus Baby.
1949 Bowman #14
The rest of the post is going to be players that I have cards for and not listed in any particular order.
1957 Topps #27
2009 Tristar Obak #68
1994 Topps 1954 Archives #174
2007 UD Masterpieces #17
1954 Topps #25
Let's finish this up with the other 3 Bonus Babies that made it to the Hall of Fame.
2005 UD Past Time Pennants #1
2005 Upper Deck Classics #42
2012 Topps Allen & Ginter What's In A Name #46