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south, southern

As a compass direction, south and southern are not capitalized:
            He lived south of Washington.
            He lived in the southern part of the state.

Capitalize each term when it is used as a proper name or as part of a proper name, and if the region is widely known:
            The Civil War pitted the South against the North.
            He moved to South Florida.
            Southern California has many lovely beaches. 

U.S. context
South, Old South
South Jersey
Deep South
southern states
Southwest, Southeast
South Florida
Southeast Alaska
Southern California
southern Maryland
south-central Iowa
southern accent
southeastern states

Other contexts
south, southern
southeast, southwest
South Pacific
South Pole, but the pole
South Sea island
South Seas (literary concept)
South Asia
Southeast Asia
Southern Hemisphere, the hemisphere
Southern Cross (Crux constellation)
southern Africa (region)
South Africa (country)
South Sudan
south magnetic pole
See also north, northern, pole, polar.