Yes.
MVPs that played on a losing team are Ernie Banks for the 1958 Chicago Cubs (record was 72-82) and 1959 Cubs (74-80), Cal Ripken Jr. of the 1991 Baltimore Orioles (67-95), and Andre Dawson of the 1987 Chicago Cubs (76-85).
Actually, it's been done twice.
Andre Dawson was the NL MVP in 1987, despite playing for the last place Chicago Cubs.
Alex Rodriquez repeated this "feat" in 2003 for the AL last place Texas Rangers.
Sammy Sosa
The Major League baseball Most Valuable Player awards were established in 1931 by the Baseball Writers Association of America and have always been called the Most Valuable Player Awards.
International League Most Valuable Player Award was created in 1932.
As a minor league baseball player, soon to be a great player, Mickey Mantle was paid $225 per month.
Pacific Coast League Most Valuable Player Award was created in 1927.
Major League Baseball All-Star Game Most Valuable Player Award was created in 1962.
Sammy Sosa
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The Major League baseball Most Valuable Player awards were established in 1931 by the Baseball Writers Association of America and have always been called the Most Valuable Player Awards.
Alex Rodriguez playing for Texas Rangers won in 2003, he also won the award in 2005 and 2007, both for the New York Yankees
International League Most Valuable Player Award was created in 1932.
As a minor league baseball player, soon to be a great player, Mickey Mantle was paid $225 per month.
NBA Development League Most Valuable Player Award was created in 2002.
Pacific Coast League Most Valuable Player Award was created in 1927.
League Championship Series Most Valuable Player Award was created in 1977.
Barry Bonds won 4 consecutive National League Most Valuable Player awards, from 2001-2004. 12 different players have won their league's Most Valuable Player award for 2 consecutive years. This includes 6 players in the American League and 6 players in the National League (including Barry Bonds in 1992-1993).
Shortstop Zoilo Versailles of the 1965 Minnesota Twins who was born in Havana.