Sorry, my bad, what we used was Bach - Suite No. 3 - Air. Apparently, it’s also known as “Air on the G string”, if that helps your decision at all. 
It’s vocal, not instrumental, but Dan Fogelberg’s “Longer” is one of my favorites. I might have the title wrong but the lyrics are along the lines of “longer than there’ve been stars up in the heavens, I’ve been in love with you”.
For returning from the Altar…may I suggestion: Monty Python’s Flying Circus Theme, which is some formal march by Strauss, I think, but would be very funny nonetheless.
The song is called “Liberty Bell,” it’s actually by John Phillip Sousa. It’s my cell phone ring.
Decorum would dictate the use of the dry, rattling final razzberry (heard at the beginnings of earlier shoes), instead of the wet flatulent variety adopted later.
That’s shows.
Another vote for Pachebel’s Canon in D for the actual processional.
For music to be played before the wedding party begins to walk down the the aisle, I’d suggest “Jesu, Joy of Man’s Desiring” (Bach).
For the recessional, Vivaldi’s “Spring” is always great. Upbeat but still classy.
I suggest “Linus and Lucy”, otherwise known as the Charlie Brown theme. It’ll make everyone smile.
I was at a wedding where they used that as the recessional.
At our wedding, my husband entered to “Also Sprach Zarathustra” (I’m almost positive I misspelled that), I walked down the aisle to “Ride of the Valkyries” and we recessed to Dick Dale & the Deltones’ version of “Hava Nagila”. It was the best 10-minute wedding in the history of weddings.
Aretha Franklin, “Say a Little Prayer”.
It’s what we used.
Ben E King Stand By Me
When the night has come
And the land is dark
And the moon is the only light we see
No, I won’t be afraid
Oh, I won’t be afraid
Just as long as you stand
Stand by me, so
Darling, darling stand by me
Oh, stand by me
Oh stand, stand by me, stand by me
I like “Hymne” by Vangelis. I had a friend who used this song–it was really beautiful!
The Vow to Thee, My Country from Holst’s Jupiter. (From his The Planets) I understand that by itself, as a hymn, it is known as Thaxted.
This page includes the lyrics, and a MIDI sample. (It sounds a lot better performed by an orchestra, though.)
I’m just finding out, though, that it was played during Princess Diana’s wedding…and her funeral. So, that might make it unusable for you.
Failing that…a few of the happier songs from Carmina Burana might do. Or Elgar’s Salut d’Amor.
The most memorable music I can recall from a wedding was quite simple. A relative of the bride sang “One Hand, One Heart” (from “West Side Story”) without accompaniment. The singer had a clear, pure soprano voice, and it was very moving.
That’s simply wonderful! <sniff>
And if not one of the happier songs, then “O Fortuna” (the one everybody knows). It’ll set the mood right. 
My brother, being somewhat narcissistic of personality, put on a musical and invited people to it as his wedding. He and his bride met 25 years ago on the stage on which they were later married, complete with a program, tickets for invitations, and a half-hour program of song, enacting… a wedding. Just prior to the vows, he sang, “Crazy Love” to his bride.
It was a trip.