If this site hasn't met all your postcode needs, here are some others that might help.
UK Postal Address Finder- A powerful Access application built on this and other data. There is a free version and a paid for version with even more features.
Postcode data mangler - Tony Wilk has written a useful utility to take the postcode data from this site and do various useful things, primarily to let you manipulate it in Excel without running into its file size limits.
PowerPivot for Excel 2010 - I haven't tried it myself but apparently this add-on for Excel 2010 will let you import the full postcode CSV file.
CSVed - A program to edit very large CSV files, so it can be used to view the full postcode CSV file.
OS Open Data - Home to the original source of most of the postcode data. There are a number of other UK geographical datasets also available for download.
Royal Mail PAF - If you find the postcode data here is not detailed enough for your needs (if you need to get address information for instance), then you probably want to be looking at the Royal Mail's PAF dataset. This generally costs money but is available for free to small charities and micro businesses
ONS postcode data - The Office for National Statistics aggregates OS postcode data and data from other sources and provides it in a variety of formats.
Postcode boundary polygons - Open Door Logistics provide free Shapefile polygons defining the boundaries of UK postcode areas, districts and sectors. They also provide software for mapping sales territories
Finally, some links to other data used on the site