WordPress provides free & premium themes for use with WordPress hosted websites:

There are limited options with free themes, but this can be upgraded later.

You can see all WordPress themes here: http://theme.wordpress.com/

Please Note: Premium themes have more features than free themes and will cost between £40 & £57+

Themes for use with self-hosted websites:

For high quality feature-rich themes there are many providers with 1000's of themes available. 

We use a number of trusted sources some of which are listed below.