If you want just the points (nodes/vertices) then use: Vector->Geometry Tools->Extract nodes.
Alternatively, if you want the edges between nodes (i.e. the result is a data set with lines defined by no more than two nodes, the total of which combine to represent the original line), then you want the "Split Features" plugin. Go to Plugins->Fetch Plugins. Then type 'split' into the search box and you should find it (you may have to enable 3rd party repositories). Install the plugin and then you will find it here: Plugins->Split Featutres.