Very often my clients ask for advice for processional and recessional music. Below are the standard selections that I like to use, and why they work well.
Family seating: Jesu, Joy of Man's Desiring
This classic music by J.S. Bach contains a beautiful 9/8 lilting melody, interspersed with a chorale melody. The great thing about this music (besides it being Bach!) is that it can be stopped at a number of points and brought to a logical close, so when the family is seated, we are ready to move on.
Bridal Party: Canon in D
This masterful piece by baroque composer Johann Pachelbel is familiar yet elegant. It is written in four bar phrases that can be ended as soon as the last member of the bridal party is in place. To get the true "canon" effect (a canon is a "round" like "Three Blind Mice", where melodies are played and then played again on top of each other), a second or third instrument is needed, like violin, flute, or cello, but it is perfectly playable as a solo.
Bride: Bridal Chorus from "Lohengrin"
This is the classic "Here Comes the Bride" with which everyone is familiar, but many people do not know that it's origin is operatic, coming from Richard Wagner's music drama "Lohengrin", and is actually sung by a women's chorus during the opera. Like the other two pieces mentioned above, it has a number of points where it can be easily ended, making it a classic and excellent choice for a processional.
Recessional: Wedding March from "A Midsummer Night's Dream" Incidental Music
The music played as the bridal party recesses at the conclusion of the ceremony is from Felix Mendelssohn's music that he composed to accompany Shakespeare's play. This joyous piece makes everyone think "wedding" immediately, and can be repeated as often as needed to accompany everyone as they exit the wedding area.
Other choices:
For those couples wanting other choices, here are some other pieces that work well as substitutes:
Processional Music (for family, bridal party, or bride): Any of the three pieces mentioned above can be switched around and used in place of each other ("Canon" for family or bride, :"Jesu" for bridal party or bride, etc..). Other choices would include the Handel "Air", Purcell's "Trumpet Voluntary".
Recessional Music: Other excellent selections include the Handel Harp Concerto, Handel's "Hornpype", and "Spring" from "The Four Seasons" by Vivaldi.