I can't remember the last time a 35+ year old was a Hart Candidate. Hard to believe Jagr was 3 years younger in 2006. I guess maybe Selanne in 2007 qualifies but he only finished 9th.
The oldest to win the Hart Trophy were Herb Gardiner (1926-27) and Eddie Shore (1937-38).. someone can compare their birthdays to see who was technically older, but they were both 35. If Ovechkin were to win it this year, he would become the oldest in NHL history.
Just scrolling through years for Finalists, I used 34 as my arbitrary cutoff:
Martin St. Louis was 35 and finished third in 2010-11
Martin Brodeur was 34 and finished third in 2006-07
Patrick Roy was 36 and finished third in 2001-02
Mario Lemieux was 35 and finished 2nd in 2000-01
Dominik Hasek was 34 and finished 3rd in 1998-99
Mark Messier was 35 and finished 2nd in 1995-96
Tony Esposito was 35 and finished 3rd in 1979-80
Jean Beliveau was 37 and finished 2nd in 1968-69
Jean Beliveau was 36 and finished 2nd in 1967-68
Jean Beliveau was 34 and finished 2nd in 1965-66
Gordie Howe was 36 and finished 3rd in 1964-65
Gordie Howe was 35 and finished 3rd in 1963-64
Gordie Howe was 34 and finished 1st in 1963-63
Doug Harvey was 37 and finished 2nd in 1961-62
Johnny Bower was 36 and finished 2nd in 1960-61
Elmer Lach was 34 and finished 2nd in 1951-52
Eddie Shore was 35 and finished 1st in 1937-38
Lionel Conacher was 35 and finished 2nd in 1936-37
Bill Cook was 36 and finished 2nd in 1932-33
Herb Gardiner was 35 and finished 1st in 1926-27
Sprague Cleghorn was 35 and finished 2nd in 1925-26
The fact that only 1 Non-Goaltender 34 or older has finished Top 3 in the last 20 years is pretty remarkable and shows how rare and hard that is to accomplish. The NHL is just way too competitive with a large international player pool these days for old guys to dominate like this. As you see, it was more commo of an occurrence, in particular for non-Goaltenders, over 50 years ago. Messier, Lemieux and St. Louis are the only ones to finish top 3 outside of Goaltenders in the last 50 years.