You can spread religions via missionaries to civs you have open borders with.
Also, there are religious civics, some of which only give you benefits if you have a state religion and the city has the state religion present.
Organised Religion: Don't need monasteries for building missionaries (nice), +25% production for buildings in cities with state religion present (sweet especially early on when you need granaries, courthouses, etc.)
Theocrarcy: No spread of non-state religion, and +2 xp for troops built in cities with state religion present
Pacifism: +100% great person birth rate in cities with state religion present. This is probably my favourite one.