Today, the two oldest players considered "active" are Jamie Moyer (46) and Randy Johnson (45) as of opening day 2009. The oldest living former baseball player is Tony Malinosky, born in 1909 and played in 1937.
While all of that might be true (or at least according to internet resources) . . . I present Dave Magadan - the "unofficial" oldest player ever to put on a major league uniform.
According to his Studio 91 card, he was born in 1862 ! Thereby making him a 124 year old Rookie (when he entered the league in 1986).
At that age it is unfair to classify him as "slow", stealing only 11 bases and chugging his way to 13 triples in 16 years in the majors.
If Studio 91 is correct then he was 139 years old when he left the game to "retire" in Tampa Florida. Good for him . . . it was about time he left the game . . .