We should first recognize that there was not one system of punctuation in use during Classical times. However, all of modern punctuation, including commas, periods, colons, semicolons, etc. are more recent, not just for Latin, but for European languages as a whole (and in fact worldwide, as e.g. Chinese borrowed the question mark).
Not only that, but word spacing too is relatively recent. Many early manuscripts lack any punctuation and word division.
In the earliest inscriptions, too, you can see a lack of word division or punctuation. Take a look at the Duenos Inscription (ca. 580–570 BCE):
However common this was, there were some variations. In a dedication to Castor and Pollux (ca. 550–525 BCE) in between "to Castor" (CASTOREI) and "to Pollux" (PODLOUQUEI) there is word division indicated by an interpunct
The interpunct was most often used for word division in inscriptions. Sometimes, there may be two dots, even three as evident from the Forum Inscription (6th century):
You may also note in that inscription that a slash
\ is used for sentence division.
Finally, because the letter I in Latin was used for both a vowel (long and short) and a consonant (having the IPA value of
j), it was not infrequently drawn particularly elongated to indicate vowel length.
Baldi, Philip 1999. The Foundations of Latin. de Gruyter.
Bodel, John 2012. "Paragrams, Punctuation, and System in Ancient Roman Script," in The Shape of Script ed. Stephen D. Houston, Santa Fe, pp. 65–92.
Sacks, David 2007. Letter Perfect: The Marvelous History of Our Alphabet From A to Z. Random.