Full disclosure -- my college friend and housemate wrote this, so I might be a teensy bit biased.
If you've seen A League of Their Own, you probably know that when American men went off in droves to fight WWII, American women stepped up to the plate (literally) to save America's Pastime, baseball. Players in Pigtails tells the story of baseball-crazy Katie Casey, who is one of hundreds of girls who tried out for (and made) the All American Girls Professional Baseball League in the 1940s. The story follows Katie's journey from her frustrations at home, failing at home ec and other "womanly" pursuits, to Chicago to try out for the new league, to the league's efforts to make "players in pigtails" more palatable to the public by making sure the girls of the GPBL were very ladylike.
My sons, ages 2 and 4, both really like this book, so don't make the mistake of thinking it's only for girls! The illustrations are whimsical and endearing, though I do have one pet peeve: in the last scene, Katie hits a grand slam home run -- but in the picture that accompanies the text, there are no base runners on the pitch, only fielders!