I'm looking to convert Park polygons from OSM into points.
The QGIS fTools Extract Nodes tool will convert a polygon to points at the vertices.
What is the equivalent function or work-flow in PostGIS?

Answer
Yo can use ST_DumpPoints(geom) to get the points listed.
Look at the example how to use it.
The result contains both the geometry and a path telling where in the polygon the point belongs. So to just get the geometry (points) do like this:
SELECT (ST_DumpPoints(the_geom)).geom
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