Below is a listing of all the parks regularly used by each Major League Baseball team. One day, all of these will have write-ups.
 
Current American League Teams

Anaheim Angels

1961      Wrigley Field (as the Los Angeles Angels) 
1962-1965 Dodger Stadium (as the Los Angeles Angels) 
1966-     Edison International Field (aka Anaheim Stadium until 1997) 

Baltimore Orioles

1901      Lloyd Street Grounds (as the Milwaukee Brewers) 
1902-1953 Sportsman's Park (as the St. Louis Browns) 
1954-1991 Memorial Stadium 
1992-     Oriole Park at Camden Yards 

Boston Red Sox

1901-1911 Huntington Avenue Grounds 
1912-     Fenway Park 

Chicago White Sox

1901-1910 South Side Park 
1910-1990 Comiskey Park 
1991-     New Comiskey Park 

Cleveland Indians

1901-1931 League Park 
1932-1993 Cleveland Stadium 
1994-     Jacobs Field 

Detroit Tigers

1901-1911 Bennett Park 
1912-1999 Tiger Stadium (Navin Field until 1938)
2000-     Comerica Park 

Kansas City Royals

1969-1972 Municipal Stadium 
1973-     Kauffman Stadium (Royals Stadium until 1993) 

Minnesota Twins

1901-1910 American League Park (as the Washington Senators) 
1911-1960 Griffith Stadium (as the Washington Senators) 
1961-1981 Metropolitan Stadium 
1982-     Hubert H. Humphrey Metrodome 

New York Yankees

1901-1902 American League Park (as the Baltimore Orioles)
1903-1912 Hilltop Park 
1913-1922 Polo Grounds 
1923-1973 Yankee Stadium
1974-1975 Shea Stadium 
1976-     Yankee Stadium 

Oakland Athletics

1901-1908 Columbia Park (as the Philadelphia Athletics) 
1909-1954 Shibe Park (as the Philadelphia Athletics) 
1955-1967 Municipal Stadium (as the Kansas City Athletics) 
1968-     Network Associates Coliseum (Oakland-Alameda County Stadium until 1999) 

Seattle Mariners

1977-1999 Kingdome 
1999-     Safeco Field 

Tampa Bay Devil Rays

1998-     Tropicana Field 

Texas Rangers

1961      Griffith Stadium (as the Washington Senators) 
1962-1971 Robert F. Kennedy Stadium (as the Washington Senators) 
1972-1993 Arlington Stadium 
1994-     The Ballpark in Arlington 

Toronto Blue Jays

1977-1989 Exhibition Stadium 
1989-     SkyDome 


Current National League Teams

Arizona Diamondbacks

1998-     Bank One Ballpark 

Atlanta Braves

1874-1914 South End Grounds I, II, and III (as the Boston Braves)
1914-1952 Braves Field (as the Boston Braves) 
1953-1965 County Stadium (as the Milwaukee Braves) 
1966-1996 Atlanta-Fulton County Stadium 
1997-     Turner Field 

Chicago Cubs

1876-1877 State Street Grounds 
1878-1884 Lakefront Park
1885-1891 Westside Park 
1891-1893 Brotherhood Park 
1893-1915 West Side Grounds 
1916-     Wrigley Field 

Cincinnati Reds

1876      Lincoln Park Grounds 
1876-1879 Avenue Grounds 
1880      Bank Street Grounds 
1890-1901 League Park 
1902-1911 Palace of the Fans 
1912-1970 Crosley Field 
1971-     Cinergy Field (Riverfront Stadium until 1996) 

Colorado Rockies

1993-1994 Mile High Stadium
1995-     Coors Field 

Florida Marlins

1993-     Pro Player Park (Joe Robbie Stadium until 1997) 

Houston Astros

1962-1964 Colt Stadium 
1965-1999 Astrodome
2000-     Enron Field 

Los Angeles Dodgers

1890-1912 Washington Park (as the Brooklyn Dodgers) 
1913-1957 Ebbets Field (as the Brooklyn Dodgers) 
1958-1961 Memorial Coliseum 
1962-     Dodger Stadium 

Milwaukee Brewers

1969      Sicks Stadium (as the Seattle Pilots) 
1970-2000 County Stadium 
2001-     Miller Park 

Montreal Expos

1969-1976 Jarry Park
1977-     Olympic Stadium 

New York Mets

1962-1963 Polo Grounds 
1964-     Shea Stadium 

Philadelphia Phillies

1887-1894 Philadelphia Base Ball Grounds 
1895-1938 Baker Bowl
1938-1970 Shibe Park
1971-     Veterans Stadium 

Pittsburgh Pirates

1891-1909 Exposition Park 
1909-1970 Forbes Field
1970-2000 Three Rivers Stadium 
2001-     PNC Park 

St. Louis Cardinals

1893-1920 Robison Field
1920-1966 Sportsman's Park 
1967-     Busch Stadium 

San Diego Padres

1969-     Qualcomm Stadium (San Diego Stadium 1969-1979, Jack Murphy Stadium
             1980-1996) 

San Francisco Giants

1882-1888 Polo Grounds (as the New York Giants) 
1889-1890 St George Cricket Grounds (as the New York Giants)
1891-1957 Polo Grounds II (as the New York Giants) 
1958-1959 Seals Stadium
1960-1999 3Com Park (Candlestick Park until 1995)
2000-     Pac Bell Park