I've pressed the button "Never show again" on the notification related to the successful connection to a VPN network.
How can I re-enable this notification?
This may be in the gconf settings for nm-applet. Try installing gconf-editor:
Then run it:
And go to /apps/nm-applet and make sure 'disable-connected-notifications' and 'disable-disconnected-notifications' are disabled (unchecked).