QGIS already has very strong analytical capabilities through its GRASS toolbox. Now, this is further extended by a new plugin that offers direct access to the Sextante toolbox. With this toolbox, QGIS can tap into 300+ functions from SAGA GIS and a number of other functions.
You can find the plugin in the QGIS plugin installer. It is still in beta, so you might still find some bugs and other problems. But the developer is very responsive, just file a bug or go to the QGIS mailing list.
Update: the plugin now also offers direct access to many of the GRASS GIS functions. This offers users not familiar with GRASS to use this functions without having to create or understand the setup of a GRASS database.
Next I am hoping for is the option to use GRASS layers with SAGA modules (or other non-GRASS tools). This is not yet implemented but the creator of the plugin has indicated he will add this later.