There are lots of books with classical repertoire for weddings - much of this music would also be appropriate for church preludes, etc. Here's some of the selections from mine -
J.S. Bach - Aria, "Bist du bei mir", BMV 508
Brahms - A Rose is Gently Blooming, opus 122 #8
Grieg - Notturno, opus 54 #4
Mussorgsky - Meditation, opus 70 #17
MacDowell - Clair de lune, opus 37 #1
To a Wild Rose, opus 51 #1
Burgmuller - Harmony of the angels, opus 100 #21
Goedicke - Elegy, opus 46 #29
Khachaturian - Ivan Sings
Schumann - Mignon, opus 68 #35
Poulenc - Sicilienne, from Suite Francais
Obviously some might need to be renamed if printed in a service bulletin (i.e. "Ivan Sings" could be renamed Andantino).
I've also play Brahms intermezzos, Bach preludes & invention, and numerous other quieter, reflective classical pieces.