1788: The Philadelphia Convention adopts a "zero compromise"; instead of counting three-fifths of slaves for apportionment of taxation or representation, slaves are not counted at all for both. This affects apportionment of Congress and electoral votes.
1823: William Crawford dies of his stroke, and does not run in 1824. This throws his OTL support to Clay, Adams, or Jackson. Adams or Jackson might win an electoral majority, averting the controversial election by the House.
1824: Henry Clay finishes third in electoral votes, and is eligible for election by the House.
Democrats never adopt the 2/3 requirement for nomination.
Democrats repeal the 2/3 requirement for nomination before 1844 (when a deadlock led to the nomination of "dark horse" James Polk).
... before 1860 (when Southern holdouts barred the nomination of Steph Douglas).
... before 1912 (when Champ Clark had a majority on the 10th ballot, but Woodrow Wilson was nominated on the 46th ballot).
1841: William Henry Harrison survives and completes his term. (Four solid years of a genuine Whig in power, instead Democrat maverick John Tyler, who broke with the Whigs in 1842.)
1854: Abraham Lincoln is elected to the Senate. (He was a leading candidate, but withdrew in favor of Free-Soil Democrat Lyman Trumbull, who became a Republican.)
1858: Abraham Lincoln is elected to the Senate. (The Democrats held a narrow majority of legislative seats and re-elected Stephen Douglas.)
1929-1950: There is no Great Depression, and the Solid South breaks down a generation sooner. (Republicans made their first gains in the South since Reconstruction in the 1920s. But these gains were swept away in the Roosevelt landslides; the process restarted in the 1950s.)
1987: Reagan mounts an effective defense of Robert Bork, who is confirmed to the Supreme Court. Important knock-on for U.S. politics: Bork would have ruled the other way in U.S. Term Limits, Inc. v. Thornton, a 5-4 decision.