I found it striking as I crunched the numbers that the average age of candidates now is much older than it used to be. In the list of ages of the leading candidates at each election below, I've put the 16 elections since 1952 (starting with 1956) in red; the 16 elections before 1852 (ending with 1848) in blue; and the 26 elections from 1852 to 1952 inclusive in green. It's clear that the middle period saw younger candidates, with those 26 elections supplying 22 of the bottom half of the table, and 4 of the top half - in fact, none of the middle 26 are in the top 30% of the table, and the high-water mark is the comparatively youthful matchup between Hayes and Tilden in 1876. Meanwhile all four elections since 2000, and all but two of the ten elections starting with 1980 (in darker red), are in the top third of the table. The earlier period was even more elderly, with only two elections (one of which doesn't really count) of the first 16 in the lower half of the table.
2016 ?Clinton? (69) + Trump (70) = 139
1984 Reagan (73) + Mondale (56) = 129
1848 Taylor (63) + Cass (64) = 127
1980 Reagan (69) + Carter (56) = 125
1840 Harrison (67) + Van Buren (57) = 124
1996 Clinton (50) + Dole (73) = 123
1956 Eisenhower (66) + Stevenson (56) = 122
1828 Jackson (61) + Adams (61) = 122
1800 Jefferson (57) + Adams (65) = 122
1832 Jackson (65) + Clay (55) =120
2008 Obama (47) + McCain (72) = 119
1988 Bush (64) + Dukakis (55) = 119
1816 Monroe (58) + King (61) = 119
1808 Madison (57) + Pinckney (62) = 119
1804 Jefferson (61) + Pinckney (58) = 119
2004 Bush (58) + Kerry (60) = 118
1792 Washington (60) + Adams (57) = 117
2012 Obama (51) + Romney (65) = 116
1876 Hayes (54) + Tilden (62) = 116
1844 Polk (49) + Clay (67) = 116
1836 Van Buren (53) + Harrison (63) = 116
1976 Carter (52) + Ford (63) = 115
1820 Monroe (62) + Adams (53) = 115
1992 Clinton (46) + Bush (68) = 114
1952 Eisenhower (62) + Stevenson (52) = 114
1892 Cleveland (55) + Harrison (59) = 114
1824 Adams (57) + Jackson (57) = 114
1796 Adams (61) + Jefferson (53) = 114
1916 Wilson (59) + Hughes (54) = 113
1852 Pierce (47) + Scott (66) = 113
1968 Nixon (55) + Humphrey (57) = 112
1964 Johnson (56) + Goldwater (55) = 111
1872 Grant (50) + Greeley (61) = 111
1948 Truman (64) + Dewey (46) = 110
1972 Nixon (59) + McGovern (50) = 109
1912 Wilson (55) + Roosevelt (54) = 109
1856 Buchanan (65) + Frémont (43) = 109
1788 Washington (56) + Adams (53) = 109
1932 Roosevelt (50) + Hoover (58) = 108
1928 Hoover (54) + Smith (54) = 108
2000 Bush (54) + Gore (52) = 106
1940 Roosevelt (58) + Wilkie (48) = 106
1888 Harrison (55) + Cleveland (51) = 106
1920 Harding (55) + Cox (50) = 105
1884 Cleveland (47) + Blaine (58) = 105
1944 Roosevelt (62) + Dewey (42) = 104
1880 Garfield (48) + Hancock (56) = 104
1868 Grant (46) + Seymour (58) = 104
1812 Madison (61) + Clinton (43) = 104
1936 Roosevelt (54) + Landon (49) = 103
1924 Coolidge (52) + Davis (51) = 103
1908 Taft (51) + Bryan (48) = 99
1904 Roosevelt (46) + Parker (52) = 98
1900 McKinley (57) + Bryan (40) = 97
1864 Lincoln (55) + McClellan (37) = 92
1860 Lincoln (51) + Breckinridge (39) = 90
1960 Kennedy (42) + Nixon (47) = 89
1896 McKinley (53) + Bryan (36) = 89
Note on methodology: I've taken candidates' ages in calendar years on election day. (Which for Warren Harding's was his 55th birthday, for all the good it did him.) In 1800 I count Adams (65) not Burr (44) as runner-up since that's who voters thought they were choosing between in November. For 1872 I've counted Greeley (61) as losing candidate even though he died shortly after the election; most of his electoral votes went to Thomas Hendricks (53) who went on to be Tilden's running mate in 1876 (they lost) and Cleveland's in 1884 (they won, but Hendricks died a few months after taking office). I have not counted third or lower placed candidates at all (thus excluding incumbent President Taft in 1912, when he was 55).
Incidentally the older candidate has won 32 times, and the younger 25 times. But those 32 include three elections which were really acclamations (1788, 1792 and 1820) so the fact that the Adamses were younger than Washington or Monroe doesn't really matter (indeed, there are good grounds for excluding those elections from my list entirely). The most recent period shows a shift of fortune in favour of (relative) youth; of the 16 most recent elections, the younger candidate has won nine and the older seven; of the last six elections, the younger candidate has won five (six out of six, if you want to count Gore as the 2000 winner).