The Churches of Rome
Ordered by their Location

The locations of all places are shown on my Google-Earth Map

There are over 900 Churches in Rome, obviously too many to review except for a few dozensl. I chose to distinguish them by their historical and artistic significance. - I threw in a few lesser known curiosities, the "secrets" of Rome! - which you'll have to find yourself.
There are only a handful non-Catholic ("a-catolico") sanctuaries in Rome, and they are art-historically unimportant. However a large synagogue (and a number of other Jewish establishments including catacombs) attest to 2000 years of Jewish presence in the city. And since 1995 there exists now an architecturally spectacular modern mosque in Rome, which no enlightened visitor should miss.
In this 2012 edition the churches are listed according to their geographical location

For a list of Rome's Churches see Wikipedia 

Churches in the various Regions of the City:

Forum Romanum and Circus Maximus

Lateran and the Colisseum

Trastevere

Santa Maria Maggiore

Northeast Via Nomentana

Fuori le Mura

The Vatican and the Sistine Chapel

Other Faiths and Oddities