Thankfully, the groom included his playlist in the description of this photo:

Theme to Star Trek (End Credits) - Trek Connection
Ready 2 Wear - Felix da Housecat - Devin Dazzle & the Neon Fever
Such Great Heights - The Postal Service - Give Up
Por una cabeza - Tango Project - Scent of a Woman
Fly Me To The Moon - Frank Sinatra
One Of These Things First - Nick Drake
The Way you Look Tonight - Hollywood: Hit Songs From a Golden Era
A Kiss to Build a Dream - Louis Armstrong - Hollywood: Hit Songs From a Golden Era
Miss Sarajevo - U2 - Passengers 1
Clocks - Coldplay - A Rush of Blood to the Head