Baseball/Rounders- According to Bill Bryson's (highly readable) "Made in America" the OED's first citation for the word "Baseball" dates from 1744.
The first American reference to a bat in the context of play dates from 1734.
Contemporary documents refer to Washington's troops at Valley Forge passing time by "playing at Base."
Bryson speculates that Baseball may have originated in America.
This is not proven but as yet it is not disproven either.