Ever? The Chicago Cubs, who have scored 91,908 runs in their history.
In a season? The 1931 Yankees, who scored 1,067 runs that year (record since 1901, records before then are wonky).
In a game? 30, by the Texas Rangers, 8/22/2007
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The most runs scored in one game by one team is 36 by the Chicago in 1897. For an AL team it's the Texas Rangers at 30 in 2007. For a combined score the most is 49 between Chicago (26) and Philadelphia (23) in 1922.
At the start of the 2008 season, the Rays team record for most runs scored in a game is 19 against the Yankees in 2006 and the Blue Jays in 2004. The Rays record for most runs scored in an inning is 11 against the Mariners in 2000.
i believe it was the cardinals the other day who scored 9 in the 7t inning
Brian Lara has scored 400* in an inning.
In the 2011 MLB season, the team that scored 13 or more runs in a game the most was the Boston Red Sox who did it 12 times. They scored 18 runs twice, 16 runs once, 15 runs twice, 14 runs 5 times, and 13 runs twice. The teams that scored exactly 13 runs in a game the most were the Texas Rangers and Toronto Blue Jays who each did it 4 times.