The licence under which the WordPress software is released is the GPLv2 (or later) from the Free Software Foundation. A copy of the licence is included with every copy of WordPress, but you can also read the text of the licence here.

Part of this licence outlines requirements for derivative works, such as plugins or themes. Derivatives of WordPress code inherit the GPL licence. Drupal, which has the same GPL licence as WordPress, has an excellent page on licensing as it applies to themes and modules (their word for plugins).

There is some legal grey area regarding what is considered a derivative work, but we feel strongly that plugins and themes are derivative work and thus inherit the GPL licence. If you disagree, you might want to consider a non-GPL platform such as Serendipity (BSD licence) or Habari (Apache licence) instead.