87 players have career batting averages of 1.000. By the way the math of baseball stats work, all of those players also have career on base percentages of 1.000.
The list of players with perfect career OBPs is longer, though, since there are more ways to get on base than just hits. The OBP list only has 47 more people on it. That means 47 people in major league history have reached base by means other than a base hit. That means they never recorded an official at-bat.
Two Yankees appear on the list of people who have 1.