Since Greece is a country that is part of the European Union, I think that they would be right to bail them out of their financial troubles. Part of the purpose for forming the EU was for just such a circumstance. They are supposed to be able to count on each other as allies.
Yes, the EU should help bail out Greece because they stand to benefit from the success of the region. Greece has a strong merchant navy that impacts much of the EU region. If Greece sees a great deal of public cuts with austerity measures, the shipping industry will be impacted through regulatory delays, slowing the economy of the entire region.