Here's a list. Hopefully it'll be a starting point:
Railroads that dissappeared during the 50's:
Chicago, St. Louis and New Orleans Railroad (1898-1951), succeeded by Illinois Central
Winona Railroad (1926-1952), unknown if secceeded or abandoned
Grand Rapids and Indiana Railway (1896-1954), succeeded by Penndel Company
Louisville Bridge and Terminal Railway (1918-1954), succeeded by Penndel Company
South Chicago and Southern Railroad (1901-1954), succeeded by Penndel Company
Chicago, Indianapolis and Louisville Railway (1897-1956), succeeded by Monon Railroad
Cook Transit Company (1947-1956), unknown if succeeded or abandoned
Pittsburgh, Cincinnati, Chicago & St. Louis Railroad (1917-1956), succeeded by Philadelphia, Baltimore and Washington Railroad
Indiana Northern Railway (1891-1959), succeeded by New Jersey, Indiana and Illinois Railroad
Railroads that began in the 50's:
Penndel Company (1954-1976), succeeded by Conrail
Monon Railroad (1956-1971), succeeded by Louisville and Nashville
Philadelphia, Baltimore and Washington Railroad (1956-1976), succeeded by Conrail
Railroads that neither began nor ended in the 50's:
Erie Railroad (1941-1960)
Nickel Plate (1887-1964)
New York Central (1914-1968)
Louisville and Jeffersonville Bridge and Railroad Company (1917-1968)
Pennsylvania Railroad (1918-1968)
Chicago and Eastern Illinois Railroad (1940-1969)
Illinois Central Railroad (1886-1972)
Michigan Central Railroad (1846-1976)
Indianapolis Union Railway (1853-1976)
Joliet and Northern Indiana Railroad (1854-1976)
Pittsburgh, Fort Wayne and Chicago Railway (1862-1976)
Fort Wayne and Jackson Railroad (1880-1976)
Cleveland, Cincinnati, Chicago and St. Louis Railway (1889-1976)
Peoria and Eastern Railway (1890-1976)
Central Indiana Railway (1903-1976)
Twin Branch Railroad (1925-1978)
Kentucky and Indiana Terminal Railroad (1910-1981)
Lake Erie and Fort Wayne Railroad (1904-1982)
Louisville and Nashville Railroad (1880-1983)
New Jersey, Indiana and Illinois Railroad (1902-1983)
Chicago, Milwaukee, St. Paul and Pacific Railroad (1928-1985)
Baltimore and Ohio (1874-1987)
Ferdinand Railroad (1911-1987)
Chesapeake and Ohio Railway (1921-1987)
Dayton and Union Railroad (1863-1989)
Southern Railway (1900-1990)
Cincinnati, Indianapolis and Western Railroad (1915-1990)
Chicago, South Shore and South Bend Railroad (1925-1990)
Wabash Railroad (1942-1991)
Muncie and Western Railroad (1902-1995)
Louisville, New Albany and Corydan Railroad (1887-2006)
Algers, Winslow and Western Railway (1927-2007)