Final answer:
Critical or realigning elections include the 1932 election of Franklin D. Roosevelt, the 1964 victory of Lyndon B. Johnson, the 1980 election of Ronald Reagan, and the 2008 election of Barack Obama, each marking significant shifts in U.S. political dynamics.
Step-by-step explanation:
Four elections that are considered critical or realigning are the ones that brought significant shifts in party allegiance and policy direction. The first is the 1932 election of Franklin D. Roosevelt, which signalled a shift towards the Democratic Party and its New Deal policies. Another is the 1964 election where Lyndon B. Johnson's victory marked a realignment towards civil rights and a more liberal social policy.
The 1980 election of Ronald Reagan ushered in a conservative realignment and a move towards free-market policies. Lastly, the 2008 election of Barack Obama was pivotal due to its impact on race and gender issues, and the beginning of a trend towards more progressive social policies. These elections led to substantial and lasting changes in the American political landscape.