There is an interesting correlation between the Norse choice of gods to rule the days and the ones the Romans chose.

Monday      lunedi     lunes      lundi
Tuesday     martedi    martes     mardi
Wednesday   mercoledi  miércoles  mercredi
Thursday    jovedi     jueves     jeudi
Friday      venerdi    viernes    vendredi
Saturday    sabato     sábado     samedi
Sunday      domenico   domingo    dimanche
lunedi: from luna, the Moon
martedi: from Mars, the Roman god of war
mercoledi: from Mercury, the messenger of the gods(1)
jovedi: from Jove, the thunder god(2)
venerdi: from Venus, the goddess of love(3)
sabato: from the Sabbath day
domenico: essentially, the day of the Lord

Why the decisions were made is still beyond me; why the fifth day of the week belonged to the goddess of love and not the goddess of, say, the harvest, or any other deity, seems to have been made arbitrarily.

It seems fairly safe to say that the Romans named the days first and then, during their conquests and fall, their neighbors and former vassal states took these ideas and made them their own.(4)

Another bit of interest is that in Italian and French, the days belong to the gods (jovedi = day of Jove), while the Spanish just use the possessive (jueves = Jove's).

Now, in German, we have:

Sonntag: like Sunday
Montag: like Monday
Diensdag: "Assembly Day"; possibly from the assembling of soldiers?
Mittwoch: mid-week, literally
Donnerstag: "thunder day"
Freitag: like Friday
Samstag: presumably like samedi
Another interesting derivation is in Sweden, Denmark, and Norway, Saturday is Lördag or Lørdag, "washing day".
(1) Odin, besides being the All-Father, was also the most informed of the Norse pantheon; he traded his eye for his wisdom, and his ravens travel around the globe for information, making him a good parallel to Mercury.

(2) Jove (Jupiter) was the leader of the Roman gods, yes, but one of the major factors of his aspect was as the god of the lightning.

(3) Frigga was the Norse equivalent of Juno. However, the Norse goddess of love (and analogue of Venus) is Freyja; the similarity of names may indicate that the goddesses were combined into one, or that Friday was named after Freyja instead. The similarity could also be meaningless and the parallel false.

(4) This is simply speculation on my part; please don't write a paper on it without backup sources.

Source for some of the days: