United Kingdom postcodes
Most addresses in the UK can be identified by house number and postcode, but the postcode database is not freely available. There are various projects related to OSM which are building a free collection of postcode to location data, among them Free the Postcode (which asks you to enter your postcode and GPS coordinates) and npemap (which lets you find your postcode on a scanned out-of-copyright map). Some data from these two collections has been imported back into OSM as the 'uk_postcode_centroid' tag, which indicates a node that is roughly the centre of a postcode prefix area (for example uk_postcode_centroid=SW1).
The postcode project most closely involved with OSM is the Postbox locator on dracos.co.uk. This uses a list of all post boxes (with the postcode area they serve) supplied by the Royal Mail and tries to map them onto OSM data. You can help by adding the 'ref' when you add a post box. See Tag:amenity=post_box for details.
There is a map of postcodes here https://dev.openstreetmap.org/~random/postcodes/
There is a table of UK towns by postcode, put together by OSM wiki people, here.
This project is possibly taking on a new direction, with the release of postcode data from the OS. Further information is available at Free_The_Postcode#UK