March 1 - (or January 3 in American date format) The date will be 1/3/37. This is likely to become an Internet phenomenon, as this date represents numerically the sociolect variety known as Leet.
June 29 - Near-Earth object 2002 LT38 will make close approach to Earth.
In the 2002 movie The Time Machine, demolitions on the moon cause the moon to break up and the earths orbit is affected, causing mass extermination of the human race.
In the Star Trek universe, the third manned space mission to travel outside of the confines of the Terran solar system, the Charybdis, takes place this year
In the Disney Channel Original Movie and the book, Zenon: Girl of the Twenty First Centery. The movie and book takes place in the year 2037.
Anniversaries
100th anniversary of the publication of J.R.R. Tolkien's fantasy novel The Hobbit
The Atanasoff-Berry Computer, arguably the first digital computer will celebrate its 100th anniversary.