Why the Catholic Church has standards for liturgical music
Catholic liturgy is not a concert, and not a personal celebration with a religious veneer. It is the worship of God by his Church, into which the wedding being celebrated is set. Music in the liturgy serves the liturgy; it does not exist for its own sake. The Church's guidelines on liturgical music exist to ensure that the music actually serves what is happening at the altar.
The two most important documents to know about are Sing to the Lord, the U.S. bishops' 2007 guidelines on liturgical music, and the Universal Norms on the Liturgical Year and on the Roman Calendar. Both teach that music in the Catholic liturgy should be sacred (composed for liturgical use), beautiful (reflecting the dignity of worship), and universal (appropriate for the whole people of God, not narrowly personal).
This is why the parish music director will often say no to popular love songs from the radio. It is not about taste. It is about whether the song was written for liturgy or for entertainment, and whether it can serve the Mass rather than compete with it.
The four (or five) musical moments in a Catholic wedding
Catholic wedding music typically appears at four moments, with a fifth in a Nuptial Mass.
The Processional. As the wedding party and bride enter, instrumental music or a hymn carries the procession. Common traditional choices include Pachelbel's Canon, Bach's Air on the G String, Wagner's Bridal Chorus (some priests prefer not to use it because of its operatic associations), Charpentier's Te Deum Prelude, and Handel's La Réjouissance. These are public-domain instrumental pieces that any parish music director will welcome.
The Responsorial Psalm. Sung between the first and second readings, this is the assembly's response to the Word of God. It is properly sung by a cantor with congregational refrains. Common settings of Psalm 128 ("Blessed are those who fear the Lord") and Psalm 34 ("Taste and see") are widely known and beloved.
The Offertory. As the gifts are brought to the altar, music often accompanies the action, whether instrumental or a hymn. This is a moment where Marian hymns like Ave Maria or Salve Regina often appear, especially if the couple plans to present flowers to a statue of Mary at this point.
Communion (in a Nuptial Mass). As the assembly receives Communion, music is sung. Common choices include Panis Angelicus, Ave Verum Corpus, and other Eucharistic hymns.
The Recessional. As the new spouses lead the procession out, joyful instrumental music (Mendelssohn's Wedding March is a classic) or a triumphant hymn carries them.
Beloved traditional hymns that work in any parish
If you want to know what music is essentially universally welcomed in a Catholic wedding, here is the short list (without reproducing copyrighted lyrics).
For processional and recessional: Pachelbel's Canon in D, Bach's Jesu Joy of Man's Desiring, Handel's La Réjouissance, Charpentier's Te Deum Prelude, Mendelssohn's Wedding March, Widor's Toccata.
For Marian moments: Schubert's Ave Maria, Bach-Gounod's Ave Maria, Salve Regina (the traditional chant), and Regina Caeli during Easter season.
For Communion or quiet moments: Panis Angelicus (especially the César Franck setting), Ave Verum Corpus (Mozart's setting is widely used), and O Sanctissima.
For the Responsorial Psalm: ask your music director. The available settings vary by parish, but Psalm 128, Psalm 34, and Psalm 33 are common wedding choices, and most parish music ministries have multiple settings of each.
All of the pieces named above are firmly in the public domain (the composers all died well before the 20th century), so reproducing them in your wedding program is unproblematic. Many of them are so widely loved that even non-Catholic guests will recognize them.
Working with your parish music director
Contact your parish music director early. At least four to six months before the wedding, ideally longer. Music ministers often have other commitments and need lead time to coordinate cantors, accompanists, and any guest musicians.
Come to the first conversation with a list of moments (processional, psalm, offertory, communion, recessional) and any pieces you have in mind. Ask the music director what they recommend for each moment. Trust their judgment about what works in your specific church. Acoustic spaces vary, and a piece that sounds beautiful in a small chapel may not work in a large cathedral.
If you want to involve a friend or family member as a vocalist or instrumentalist, ask early. Most parishes welcome this with appropriate coordination. Your guest musician will need to rehearse with the parish accompanist and use settings the parish supports. Bringing a guest musician without prior coordination almost always leads to problems on the wedding day.
Common mistakes to avoid
Don't assume your favorite song from the secular world is appropriate. "All of Me," "A Thousand Years," "Marry Me," and similar popular love songs are not appropriate during the Mass itself. They can be played at the reception. They cannot be played during the wedding liturgy. This is not the music director being difficult. It is Church teaching.
Don't surprise the priest with music he hasn't approved. Some couples try to negotiate around the music director by approaching the priest separately. This rarely works. The priest will defer to the music director on most music questions and will be uncomfortable being asked to override their judgment.
Don't underestimate how much music a wedding actually contains. Couples often arrive thinking they need three pieces and are surprised to learn the wedding contains six or seven musical moments. Plan accordingly with your music director.
Don't cut corners on the Responsorial Psalm. The psalm is sometimes treated as an afterthought; it should be one of the most carefully prepared musical moments, because it is the sung Word of God in the middle of the Liturgy of the Word.