Thanks for your prompt reply expharm.
I installed it & configure it with SSL & authentication and it worked.
But then problems :-( I am using a simple gmail account (small customer and I didn't need to set up a Google apps account).
Gmail got all funny, and start suspending the account every couple of incoming forms, asking me to provide new pass every time.
Now I am lost somewhere between gmail's 2-step verification and "application specific passwords", so the battle is far from over.
I think my problem is that I access the account from a different country from the WP-Mail-SMTP authentication (as server is located abroad) and this looks suspicious.
Yet, this "contact form not sending problem" is affecting more than 5 of my sites with different hosting providers, WP versions and form plug-ins, so my best guess is that email providers (gmail, yahoo...) probably implemented some new rules on the incoming emails in order to fight spam. Could this be an explanation?