Romain,

Different countries got into difficulty for different reasons. Portugal, Greece and, to an extent, Italy borrowed to keep paying for inefficient public sectors. Ireland's government promised a massive bailout for its banks. Spain tried to avoid doing this, but ended up having to bail out its provincial banks.
(This is, of course, a simplified answer, but I think it captures the basics!)

Underlying all these was the odd fact that until 2007 nobody really differentiated between different Eurozone countries' debt - it was all just in Euros and attracted the same rate of interest.

Hope this helps
Chris West