An early version of the alphabet used by some ancient people of Italy included the letter zeta. Zeta is the sixth letter of the Greek alphabet, following alpha (Roman A), beta (Roman B), gamma (Roman C), delta (Roman D), and epsilson (Roman E). Where zeta was used in Italy, it kept its 6th place.
The third letter of the Latin alphabet was a C. This was pronounced hard, like a K (voiceless velar plosive). The letter K of the Roman alphabet was pronounced like a K, as well. K was rarely used, however, and was usually (perhaps, always) followed by the vowel A, as in Kalendae, from which we get the English word calendar.
The letter C also served for the sound of G -- a reflection of its origin in the Greek gamma. The difference is not so great as it looks since it is what's referred to linguistically as a difference in voicing: the G sound is the voiced version of the K or hard C. [The praenomen Caius is an alternative spelling of Gaius; both are abbreviated C. See: How to Read a Roman Name.] When the C and G sounds were separated and given different forms, the second C was given a tail, making it a G, and moved to the sixth place in the Latin alphabet, where the zeta would have been had it been a productive letter for the Romans, which it was not.
The Latin alphabet had 21 letters in the first century B.C., but then, as the Romans became Hellenized, they added two letters at the end of the alphabet, a Y for the Greek upsilon, and a Z for the Greek zeta, which had no equivalent in the Latin language*.
Sources: "On the Origins of the Latin Alphabet: Modern Views, by Arthur E. Gordon. California Studies in Classical Antiquity, Vol. 2, (1969), pp. 157-170.
*"Transliteration or Transcription of Greek," by Gerald P. Verbrugghe. The Classical World, Vol. 92, No. 6 (Jul. - Aug., 1999), pp. 499-511.
Also see: "Review by D. M. Jones of L'alfabeto e pronunzia del latino." The Classical Review, New Series, Vol. 8, No. 3/4 (Dec., 1958), pp. 292-293.
