My parent's address structure is:

House Name, Road, Village, Town, County, Country (if applicable) Post Code.

My address structure is:

Flat Number - Building, Road, City, Country, Post Code

Some multi-input address forms require that I enter both a city and a county, which in the case of Londoners means you end up putting London twice. The only important parts of the address (for most uses, including credit card processing) are recipient name, house/flat name/number (actually, not sure about this - it might not be necessary) and Post Code.

So why not just have explicit inputs for those fields which are always required, and allow a more fuzzy input for everything else in the form of a textarea? It also means you're more likely to be able to deal with addresses in countries that use slightly different systems.