Some Renaissance and Medieval faires are set in a particular period, others are more general. However, when everyone is finally assembled, performers and patrons alike, the style of clothing alone can span several hundred years. More than any other reasons, this sort of anachronism tends to be the product of limited wardrobes and varying tastes. The same phenomenon applies to music. Just as most patrons would not recognize period instruments, neither would they recognize period music, harmonies, and meter. A John Denver song might feel just as reasonable as one by Henry VIII if played appropriately.
I am a balladeer in the broadside tradition, so it may be difficult sometimes to peg me down to a style. I try to mix and match anything and everything that I can to make it oddly entertaining for listeners.
There are several faire musicians with web sites on the internet, here are a few of my favorites:
The Bilge Pumps: funny pirate's that sing very loudly
Boru's Ghost: Celtic inspired, but they go a little bit further
The Counterfeit Bards: a quartet of musicians with a Celtic lilt
Dustin Cooper: traditional European and Middle Eastern music
Howl-O: a singing and playing duo with a special spark
Lord Kerridwynn Bard of Ages: a bard that play's a lot of different instrument
Modern Bard: A repository of listings of musicians and their works
Queen's Gambit: A nifty celtic group
Renaissiance Music Podcast: Weekly MP3 broadcasts of ren faire music
Renradio: an internet based radio stream