Well it depends. Women had a limited form of citizenship. They were not allowed to vote, but often participated in public life behind the scenes. Influencing their husbands, funding building projects or similar projects. Their rights changed over time. In the earlier Republic women were basically the property of their husbands (or their fathers if they were unmarried), later on they gained the right the engage in business or obtain a divorce.
Slaves could be given their freedom although this did not automatically grant them citizenship, and lacked the opportunity for instance to run for office. Children of freedmen or women however were born as free citizens.
Client states or allied states of Rome also had a limited form of citizenship, as they did not for example have the right to vote. Newly conquered territories of Rome were gradually as the years went on granted rights and citizenship. Allies could for example be granted the Latin Rights, which included rights to own land in Latin territories, rights to marry with a citizen of a Roman city, and they were protected under Roman law. It was usual for towns or city's to be granted full citizenship either as a gift or reward.