Other popular wedding songs (some kind of overused): Looking Through The Eyes Of Love (Carole Bayer Sager & Marvin Hamlisch) To Each His Own (another oldie that's been covered recently by contemporary artists) Amazed (sung by Lonestar) Endless Love (sung by Lionel Richie and Diana Ross) The Prayer (Carole Bayer Sager & David Foster) The Rose (by Amanda McBroom, recorded by Bette Midler) Unchained Melody (On the charts in the 1950s, '60s, '90s, and 2000s) Hawaiian Wedding Song Ebb Tide - another standard Not as "folky" as some of Tom's others, and a great wedding song: Outward Bound (Tom Paxton)
And I know you're not looking for folk songs, but you really should check out John Prine's song (duet with Nanci Griffith, I think) "In Spite Of Ourselves" (if only for the reception).