I think Explode lines would be the the noob-solution through the SEXTANTE toolbox.
QGIS Geoalgorithms > Vector geometry tools > Explode lines. Unfortunately, it does not seem to work at the moment, i get an error message only.
Traceback (most recent call last):
File "path/.qgis//python/plugins\sextante\core\GeoAlgorithm.py", line 145, in execute
File "path/.qgis//python/plugins\sextante\algs\Explode.py", line 58, in processAlgorithm
features = QGisLayers.features(layer)
NameError: global name 'layer' is not defined
A working solution is the
Split Feature-Plugin from the "contributed" repository, which does the job for me.
In general I prefer sextante functions over separate plugins, cause the workflow with sextante is so much faster and produces no junk-files of intermediate steps (provided it works).
Unfortunately, a lot of plugins were not moved to the official plugin repository yet, but are still only available through the "contributed" plugin repository: http://pyqgis.org/repo/contributed, which was removed from the default repositories list with version 1.8.
There you can download them individually and unzip them in your .qgis/python/plugins folder OR you add this address to your plugins repository list:
Plugins -> Fetch python plugins -> Tab "Repositories" -> Add ... -> enter a name and the url.