All facts are from http://www.canadianbaseballnews.com/.
June 13, 1999: Cal Ripken gets six hits and scores 5 runs for the Baltimore Orioles against the Atlanta Braves.
June 14, 1952: Warren Spahn strikes out 18 in a 15 inning game for the Boston Braves.
June 15, 1980: Jorge Orta of the Cleveland Indians hits six singles in one game.
June 16, 1978: Tom Seaver becomes the first Cincinnati Reds pitcher to throw a no-hitter at Riverfront Stadium.
June 17, 1880: The second perfect game in MLB was thrown (the first came in June 12).
June 17, 1915: George Zabel makes the longest relief appearance in MLB history when he relieves an injured starter in the first inning and goes on to pitch 18 1/3 innings.
June 18, 1970: Willie Mays gets his 3,000th hit.
June 19, 1977: Jim Colborn of the Kansas City Royals pitches the first no-hitter at Royals Stadium.