In music, Common Time refers to the 4/4 time signature. It means that each bar (measure) of music has four beats, each beat can be divided into two equal parts, and that a beat is equal to a quarter note. It's so common that the notes (in American English at least) are pretty much named for it. Why else would a 'whole note' be four beats and everything else taken as fractions?
For some reason, 4/4 time is used in the overwhelming majority of rock and pop songs, to the point that it gives an impression of no other time signatures existing. A well-known joke among jazz bands is about a newbie trying (and failing) to read a piece written in 7/8 time, counting the beats "one - two - three - four - five - six - se - ven," being all too accustomed to 4/4 time. Classical music is rather more diverse in meter, with 2/2 ('Cut time'), 3/8 ('waltz'), 6/8, and 3/4 being quite common.
Listing examples here is rather pointless. For exceptions, see Uncommon Time.
Not to be confused with the poetic rhythm of Common Meter.