Hey, all; I'm kind of new to this whole thing, but I had a list of historical events where subsequent history hinged on certain happenings in those events, and where sometimes you can even trace entirely divergent paths from one point in OTL -- struck me that whichever held the most potential for an ATL could be decided by you, and grown from there.
...so, here's my list:
1. In early 1799, then-Vice President Thomas Jefferson is identified as the author of the Kentucky Resolution; Congress immediately sets in motion procedures to impeach him for treason against the United States.
2. In February 1800, Alexander Hamilton is laid low by a sudden illness, and so is unable to convince Federalist electors who to vote for; as a result, the planned Democratic-Republican ticket for that year is flipped, and, thanks to the Electoral College, Aaron Burr becomes President, with Thomas Jefferson remaining Vice President for another four years.
3. In 1817, physician Christian Stockmar decides to head the medical team monitoring the health of Princess Charlotte of Wales, King George IV's only legitimate child, during her second pregnancy (the first having been a miscarriage); as a result, she does not die after the delivery, giving birth to a healthy male heir to both the British throne and her husband, Leopold of Saxe-Coburg-Saalfeld (who, in OTL, after Charlotte's death accepted the offer of Belgium's throne to become King Leopold I of that country).
4. Before the funeral of Representative Warren R. Davis, Richard Lawrence purchases two pistols not known for being vulnerable to moisture and, on the day, aims for President Andrew Jackson's head and neck before firing; as a result of Lawrence's unusual diligence, Jackson is killed on January 30, 1835. Vice President Martin Van Buren succeeds him to the office.
5. In March-April 1840, William Henry Harrison remains healthy and hale, rebuffing office seekers attempting to take advantage of the Jacksonian spoils system, and eventually presiding over a special session of Congress over a dangerous lack of federal funds on May 31st. Vice President John Tyler remains on his plantation in Virginia throughout this whole affair.
6. On July 4, 1850, Zachary Taylor decides to neither eat the cherries nor drink iced milk, instead gorging himself on fine Kentucky mash (which would not spoil so easily). His advisors are alarmed at his subsequent drunkenness during the Washington Monument's groundbreaking ceremony, but he gets over it, and sticks to his guns against the planned Compromise of 1850.