The all time MLB record is 17 consecutive plate appearances reaching base by Frank Ward in 1893. Ward got 8 hits, 8 walks, and hit by a pitch once. The modern day MLB record is held by Hall of Famer Ted Williams who reached base in 16 consecutive plate appearances in 1957. He got six hits, was walked 9 times, and hit by a pitch once.
Cal Ripkin
1988 ... the Orioles lost an MLB record 21 consecutive games to start the season.
Cal Ripken Jr.
The record is tied between the New York Yankees(1914) and the Tampa Bay Rays (2009). The record is set at 19 consecutive games.
Most team doubles in a MLB season is 376 by the Texas Rangers in 2008 as of today the Toronto Blue Jays have 140 so far after only 61 games so they are on pace to match that record
Lou Gehrig's consecutive games played record was broken by Cal Ripken, Jr. on September 6, 1995 against the Anaheim Angels when Cal played in consecutive game number 2,131. Cal would go on to play in 2,632 consecutive games, a mark that may never be broken.
Cal Ripken Jr.
45 consecutive outs by Mark Buehrle in 2009
The team record for most consecutive games with at least one run scored (i.e., most consecutive games not being shut out) is 308, set by the Yankees between August 3, 1931, and August 2, 1933.
Check out the 'Consecutive Games Played Streaks' link on this page to see the 15 longest consecutive games played streaks in MLB history.
The record for the longest home run streak in MLB history is eight consecutive games, achieved by Ken Griffey Jr. in 1993 and Don Mattingly in 1987.
Steve Garvey, 193 Games.