LeBron links to a study claiming the economic benefits of the single currency accrued mainly to Greece, Portugal & Spain.
I decided to look at the issue through the lens of real per-capita GDP via Angus Maddison's dataset and take a longer view than just the post-euro period.
Here's what I found (clic the pic for an even more wonkish image):
Ireland, Spain, Portugal and Greece were all growing fast relative to Germany (and France which is not on the graph) well before the introduction of the Euro. Ireland and Spain take off somewhere around 1990 and the intro of the Euro in 2000 does not speed up their trajectory. Portugal actually falls further behind Germany in the Euro era. Greece is the only country of these 5 whose catch-up to Germany accelerates with the intro of the Euro.
The data used can be found here.
It is also interesting to note that Greece, Portugal & Spain surged relative to Germany from 1960 - 1974, then stagnated till the end of the 1980s.