What is the highest score ever recorded in a baseball game

On June 8, 1869, the Niagara University baseball team defeated Columbia 209-10 in the highest-scoring baseball game ever.
According to The Baseball Timeline by Burt Solomon the highest scoring game between two professional teams in history took place on July 5, 1869. The Atlantics of Brooklyn beat the Athletics of Philadelphia, 51-48, in a game witnessed by 15,000 people at the Capitoline Grounds in New York.

The all-time MLB record for most runs scored in a single game is held by the Chicago Colts (now the Cubs). On June 29, 1897, they beat the Louisville Colonels, 36-7. The modern MLB record is 30 runs, set by the Texas Rangers in 2007, when they beat the Baltimore Orioles 30-3, on August 22nd of that year.

The most total runs scored in a single game is 49--the Cubs beat the Phillies, 26-23, on August 25, 1922.

June 19, 2000, New York Yankee's defeated the Boston Red Sox's 22-1 in the highest scoring game in that rivalry.