Yes. There is no requirement for particular music, but you might want to consider theme, age of your guests, and what you are expressing through your music.
That may depend on the location and type of venue. Family may also have opinions if any of them are funding the event. Some people prefer traditional music and others may want items which have a special meaning for the couple marrying.
Ask the people concerned.
Synagogue music
Arbubeebaba
Mendelssohn's Wedding March is the traditional piece played at weddings.
The recessional music was Walton's Crown Imperial.
it is played on Japanese holidays, dances, and at a Japanese wedding
At her wedding. While the pagan music was being played, she heard heavenly music in her soul.
As far as any music being allowed at a civil wedding, you can have any music you want- so long as everyone in the wedding party agrees and there is not a noise ordinance banning music over a certain decible level. You could have the heaviest metal band music if you desire.
Canon in D - johann pachelbel
People use music for entertainment and to celebrate in ceremonies. For example, games are for entertainment, and you can't find any Pokemon games without music. Also, "Wedding March From 'Midsummer Night's Dream'" is played in weddings, and "Happy Birthday" is played at birthday parties. Can you imagine entertainment and parties without music?
I don't know about Princess Di's wedding, but there is a classical piece called The Planets.
As with any type of music, at any appropriate time.
Honestly, any kind of music can be played on a synthesizer.