Could you also clarify what you mean by "ancient Athenian?" In the Archaic period, Athens was, like most Greek city-states, fundamentally a narrow oligarchy. Even after the "birth" of democracy in Athens in 509 BCE, oligarchic institutions generally persisted in many aspects of society. But by the second half of the 5th century, Athens was not only a democracy in the strictest sense of the word, but in fact what we call a "radical democracy," in that the most important decisions of the state were conducted in the assembly by acclaim--that is, by popular vote. The assembly agenda was steered by the small council (boule), whose 500 members were chosen by lot from all four property classes, from all ten citizen tribes, and from all the constituent demes of Attica. It was incredibly democratic, much more so than any modern government to my knowledge.

Even so, prominent men still managed to wield political influence. The classic example is Perikles, a blue-blood who wielded influence through his continuous occupation of one of the ten slots for generals, which was still an elected position. A counter-example is Kleon, a nouveau riche who also used the generalship as an effective platform. Both men were very effective speakers and swayed the demos more or less to their will during their heyday, despite the robust democratic institutions.

For Perikles, a good primary source is Thucydides. For Kleon, see especially Aristophanes Knights. In general on the topic, see Josh Ober, Mass and elite in democratic Athens : rhetoric, ideology, and the power of the people (Princeton 1989), and The Athenian revolution : essays on ancient Greek democracy and political theory (Princeton 1996).

Could you clarify exactly what you mean by the "oligarchical" practices of the Athenians?

Other responses focus on Athens but it's also worth saying that other societies including norse and celtic ones also had a system of slaves/thralls. In some cases people might not be obvious slaves but also not qualify as free (think serfs).

What proportion of the population was free in various societies is often not very clear - whether free men means the bulk of society with a few slaves or whether actually the 'free' were a relative elite. But I'm not sure what specific societies you think were more democratic than Athens in its democratic period.