This is a surprisingly short section at the moment, given the subject.
After Woodrow Wilson had a stroke in 1919, his wife pretty much took over, though Thomas Marshall, his Vice President, was supposed to, under Article 2, Clause 6 of the US Constitution. Wilson's advisors and wife disliked Marshall both personally and politically; he found about Wilson's stroke, but on advice from his aide he decided not to press the issue and cause a damaging (not to mention possibly precedent-setting, as these things tend to be) rift in the executive branch.
Franklin Delano Roosevelt, in addition to being elected to four terms as President (though he barely served any of the last one), was also the Democratic Party's Vice Presidential nominee in 1920, under James Cox, against Warren G. Harding and Calvin Coolidge. He and Cox were quite decisively smashed, 404 electoral votes to 127; oddly enough, both Cox and Harding were Ohio newspaper publishers, and used those businesses to help get elected Governor and Senator, respectively.
Since Robert F. Kennedy was assassinated while running for President, every candidate has had Secret Service protection, usually beginning in early February of the year of the election. However, due to the volume of hate mail he was receiving, Obama received it in May 2007; it's not clear who requested it, as some sources say it was Dick Durbin, his fellow Senator from Illinois and the Majority Whip, and others say he himself asked.
Grover Cleveland won the popular vote three times in a row, from 1884 to 1892, though in 1888 he lost the electoral vote to Benjamin Harrison. He remains the only president to serve non-consecutive terms, and one of very few to win after losing.
Richard Nixon served several terms in the House and nearly half of one in the Senate from California, and had it as his official state of residence and representation in 1960, but in 1968, when he won the Presidency after six years of mostly keeping quiet, he was living in New York. In 1972, he changed it back to California, which makes home state statistics for Presidential elections a little hairy.
Seven Presidents have previously served as generals in the US Army: George Washington, Andrew Jackson, William Henry Harrison, Zachary Taylor, Ulysses S. Grant, Rutherford B. Hayes, and Dwight D. Eisenhower. Eisenhower and Taylor were particularly apolitical while in the military; Eisenhower because he felt he should not participate in it while serving, and Taylor held several positions on both sides of the aisle, to the extent that he cared at all. Both parties recruited them furiously to run for President on their ticket after the generals' most important and famous wars were over (World War II and the Mexican-American War, respectively), and the Democrats failed in both cases. Eisenhower, feeling that Democrats were promoting collective authority at the expense of individual liberty, ran and won as a Republican in 1952, and Taylor ran and won as a Whig in 1848. Zachary Taylor was the first President to have it as his first elected office, though Washington's post as Commander-in-Chief of the Continental forces, to which he was appointed by the Continental Congress, arguably does not count as an elected position. Taylor was also the last Southerner by birth (born in Virginia, official home state Tennessee) to be elected President until Woodrow Wilson in 1912, who was born in Northern Virginia (which was, at that point, culturally similar to the rest of Virginia) and officially resided in New Jersey, and the last by residence until Jimmy Carter of Georgia in 1976.
Usually, after you leave the Oval Office, your political life ends, partially because anything else is a step down and partially because even, say, a single term as Vice President is tiring. However, a few Presidents have served in other capacities after the end of their term(s): William Howard Taft served as Chief Justice from 1921 to 1930, John Quincy Adams was redistricted into three different districts in Massachusetts from 1830 to 1848, Andrew Johnson represented Tennessee in the Senate before and after the Civil War. In addition, John Tyler was elected to the Confederate Congress twenty years after his time in the White House (though he died before being sworn in) and Walter Mondale very narrowly missed being elected to the Senate from Minnesota in 2002, after Paul Wellstone died in a plane crash shortly before the election and Mondale was hurriedly put on the ticket against Norm Coleman, who later lost even more narrowly to Al Franken.