A different question made me wonder what is the norm for Indo-European with regard to pro-drop? I know Italic languages generally do it, while Germanic languages generally don't. What about the rest of Indo-European languages? Do we suppose Proto-Indo-European did it?
Bonus question: are there any Indo-European languages that have developed a topic-prominent structure?
Hittite, Sanskrit, Greek, and Latin all usually omit subject pronouns unless the subject is somehow emphasized (although I believe it's somewhat more complicated than this in Hittite, in that some intransitive verbs, but not all, always do appear with subject clitics.) Presumably PIE was similar. The fact that there are clear cognate sets for the first- and second-person pronouns but not for a third-person pronoun also points in this direction.
It stands to reason that Germanic languages, and other IE languages that require explicit subjects, developed this feature because of the loss or syncretism of personal endings on the verb. This is borne out by the fact that French requires subject pronouns (or proclitics) while Spanish and Italian don't, since in French, many verbs have a single form for four out of the six person-number combinations, while in those other languages the verb ending usually indicates the subject unambiguously.
As for the topic-prominent question: Ancient Greek is somewhat topic-prominent in the sense that its word order largely depends on information-structural/discourse-pragmatic categories rather than syntactic ones, so that clauses tend to be organized in a Topic-Focus order (rather than SVO, SOV or whatever). It also allows clause-external topic NPs preceding a clause with its own subject NP, just like e.g. Japanese sentences of the form "That palm tree (topic) leaves (subject) are big" (example from Wikipedia), though these aren't very frequent.
Regarding the bonus question, contemporary variants of spoken French, for instance the dialect of French you would expect urban dwellers in their 20s or early 30s to speak, is arguably topic prominent, with the subjects and/or objects rarely sitting in their canonical position but rather in right or left dislocated positions. This preeminence of subjects in topic positions fits very awkwardly with the syntax of standard French, which rigidly requires a subject for any finite verb, so the usual result is that the subject is left-dislocated and a resumptive pronouns shows up right next to the finite verb, usually in a morphologically reduced form. It also features clause-external topic NPs, as in TKR's answer about Ancient Greek.
Written examples are by nature hard to find for these spoken constructions, but the official title of the number one hit of the summer 2006 is a good example.
Zidane y va marquer (to compare with the standard Zidane va marquer).
Gloss: Zidane TOPIC 3rd-person-singular Future score. Zidane is going to score
Here, Zidane sits in topic position and the canonical subject position required by French is filled with a morphologically reduced 3rd-person pronoun.
Here is an example from my own experience (from 2012).
Les gens de notre génération, c'est toujours les pères, kizont du mal à communiquer avec (to compare with the standard Les gens de notre génération ont toujours du mal à communiquer avec les pères).
Gloss: People of our generation TOPIC it is always the fathers FOCUS 3rd-plur-have difficulties to communicate with. People of our generation always have difficulties communicating with fathers.
Listening to any French radio marketed to youths or watching contemporary French movies will yield dozens of other examples.
I'm very skeptical about the very notion of pro-drop it is not a feature of syntax but rather of text. However, a typology of subject marking across IE languages is not a bad idea.
Slavonic languages generally have rich enough verbal morphology not to need explicit subject marking. Yet, they vary in the degree they mark subject external to the verb. In a language like Czech, using the pronoun is similar to raising in English, whereas in Russian it is pretty much obligatory.
