[Possibly?] Another One For Your Geographers: UK Postcodes
Data output options: HTML, XML, CSV, JSON, RDF.
An API for Codepoint Open. Shows the Latitude, Longitude, Easting, Northing and Local Authority details (county, district, ward) for a given point. Also shows nearest postcodes to a postcode and allows reverse geocoding (lat/lng to postcode)
Apparently does not include data for Northern Ireland postcodes so perhaps the name 'UK Postcodes' is a little inaccurate.
Edit: Link: UK Postcodes | Open data for postcodes