It depends on the language obviously. For English, I can tell you only about those which are the same in Italian and French: Sunday (ok, it's Domenica here meaning Day of God, but you know the Sun represents God), Monday and Saturday.
Philosopher Boëtius (470-525 A.D.), as it was pretty a trend at those times, matched the 7 planets of the now-called Solar System he knew with the 7 notes, starting from the Moon (that he considered a planet) for it was the closest to Earth:
Moon – D
Mercury – C
Venus – B
Sun (not actually a planet, but Boëtius thought it moved around Earth anyway) – A
Mars – G
Jupiter – F
Saturn – E
Then, putting the notes in order so that they were constantly separated by a rising "fourth" tune distance [you need to know musical notation a bit at least to understand this; and I might have translated it from Italian improperly though], he obtained this sequence: D G C F B E A, corresponding to Moon, Mars, Mercury, Jupiter, Venus, Saturday, Sunday.
In Italy and France (as well as in other countries) the week days are named as:
Moon-day (lunedì, lundi)
Mars-day (martedì, mardi)
Mercury-day (mercoledì, mercredi)
Jupiter-day (giovedì, jeudi)
Venus-day (venderdì, vendredi)
Saturn-day (sabato, samedi... however this two rather come from Hebrew "Sabbath" most likely)
Sun-day.
As Rochelle wrote, the English (and German) week days get their names from Nordic mythology – those, I really don't know who chose them and their order. Hope this helps anyway. ;)