(I use U.S. presidents as one example; you could easily apply the venerable Table to a whole host of subjects.)
Let's start easy.
1. George Washington: the first president, the "dollar bill guy." We'll assign him H for Hydrogen - the first element on the table, atomic number 1, just 1 lonely electron. Easy peasy, lemon squeezy. Let's move on.
2. John Adams: Pa for Protactinium. Also for PA, as in Pennsylvania - the first president to reside at 1600 Pennsylvania.
3. Thomas Jefferson - Th for Thorium. Also for Thomas. Or Mo for Molybdenum, and Monticello.
4. James Madison - Dy for Dysprosium. And for Dolly, his exceedingly popular wife.
5. James Monroe - Md for Mendelevium. And the Monroe Doctrine, a famous assertion on colonization.
6. John Quincy Adams - Co for Cobalt. Adams broke ground on the C&O Canal, now a national park and lovely piece of land.
7. Andrew Jackson - O for Oxygen, and Old Hickory, his nickname.
8. Martin Van Buren - V for Vanadium. And Van.
9. William Henry Harrison - Uuo for Ununoctium. Who knows what the heck Ununoctium is? And who remembers William Henry Harrison?
10. John Tyler - Ti for Titanium. Also for the slogan used in his campaign: "Tippecanoe and Tyler Too"
11. James Knox Polk - Po for Polonium. And Polk.
12. Zachary Taylor - Re for Rhenium. Also two letters in his nickname, "Ol' Rough and Ready".
13. Millard Fillmore - No for Nobelium, and for the Know Nothing, or American, Party, which supported him for president in 1856.
14. Franklin Pierce - Ra for Radium. And for Railroad, which Pierce tried to expand across the south.
15. James Buchanan - Si for Silicon. And Single - he was the only president who didn't marry.
16. Abraham Lincoln - Al for Aluminum. And his initials.
17. Andrew Johnson - I for Iodine and Impeachment - he was the first of two U.S. presidents (second: Clinton) to be impeached.
18. Ulysses S. Grant - S for Sulfur. And because the "S" as his middle initial was an accident - the congressman sponsoring him for the naval academy inserted an S erroneously, and Ulysses liked it so much that he kept it.
19. Rutherford B. Hayes - Ba for Barium. And Ban, as in alcohol and liquor - his wife convinced him to ban all that fun stuff in the White House.
20. James Garfield - Ca for Calcium. And Cat. As in the comic strip character.
21. Chester A. Arthur - F for Fluorine and for Federal immigration, as he was the one that enacted the first general Federal immigration law.
22. Grover Cleveland - Mg for Magnesium. And it kind of reminds you of Mugwumps, his supporters in the presidential election.
23. Benjamin Harrison - Bi for Bismuth and Billion. In his administration, for the first time except in war, Congress appropriated a billion dollars in appropriations.
24. Grover Cleveland - Ga for Gallium. And Gap - he was the only president to take office, leave office for a gap of four years, and then run again and win.
25. William McKinley - Er for Erbium, and Ear to the ground - "Uncle Joe" Cannon, later Speaker of the House, once said that McKinley kept his ear so close to the ground that it was full of grasshoppers.
26. Theodore Roosevelt - Te for Tellurium, and for Teddy bear.
27. William Howard Taft - Hf for Halfnium. And hair, facial. He was the last president to have facial hair.
28. Woodrow Wilson - Es for Einsteinium. Einstein published his general theory of relativity during Wilson's administration.
29. Warren Harding - Sg for Seaborgium, and Suffrage. His was the first presidential election in which women could vote.
30. Calvin Coolidge - Np for Neptunium. And Notary Public. His dad, a notary public, swore Coolidge in to the office by the light of a kerosene lamp.
31. Herbert Hoover - Gd for Gadolinium, or Great Depression.
32. Franklin D. Roosevelt - Fr for Francium. Also for his initials, or for FeaR, as in his famous quote, "We have nothing to fear but fear itself."
33. Harry S. Truman - B for Boron, and for Bomb. As in the atomic.
34. Dwight D. Eisenhower - Ds for Darmstadtium or Desegregation, which he championed. Or Li for Lithium, and also his campaign slogan, "I Like Ike."
35. John F. Kennedy - Cu for Copper and Cuba.
36. Lyndon B. Johnson - Na for Sodium, and Nam, as in Viet.
37. Richard Nixon - Cr for Chromium. And Crook, as in "I am not a Crook."
38. Gerald Ford - Ge for Germanium. And Gerald.
39. James Carter - Pb for Lead, but also Peanut Butter. (I almost went with Mn for Manganese, since his VP Mondale is from Minnesota - MN - but decided to play on the peanut association.)
40. Ronald Reagan - Cf for Californium. For, well, California.
41. George H.W. Bush - Nb for Niobium. Its atomic number is 41.
42. Bill Clinton - Rh for Rhodium, because he was a Rhodes scholar.
43. George W. Bush - W for Tungsten. And for W.
44. Barack Obama - Am for Americium. Because hopefully he can bring America back in to favor with the rest of the world, and make it a better place to live.
For more information about each president, check out the White House's site on the topic.