Greece was the first eurozone country to require a bailout, receiving 110bn euros last may from the IMF and the EU. It may also require another bailout, with talks of a figure around 172bn being required for the second rescue package. This second bailout is a rather contentious issue however, with Germany and the ECB disagreeing on the requirements that will have to be met in order for Greece to receive the aid.
Reasons for the bailouts
The biggest problem for the Greek government is that of tax evasion leading to a high budget deficit and therefore high overall debt. One in three Greeks are regularly evading tax, and the government's budget deficit is around 22m euros annually; interestingly around the same amount that the government is losing in tax revenue due to the high levels of evasion.
Another of the problems was that Greece were effectively lying about the levels of debt they had, meaning that the EU authorities didn't know how severe their problem was, and so by the time they were made aware it was too late. This calls for a reform of the way in which government deficits are measured and the transparency of the government's budget condition.
Ireland took 85bn euros last year from the EU and the IMF. It has also had a total of 5 bank bailouts, and there is a risk of default if the banking sector doesn't stabilise.
Reasons for bailouts
Ireland had the highest levels of growth out of any EU country before the recession, and it fell the hardest (as shown in fig 2.1 of the extract). One argument as to why Ireland was hit so hard in the global recession is that it did not have any sort of control over monetary policy or its exchange rate. While it is true that this should affect all EU countries, Ireland was growing much faster than them so the effects were more pronounced.
Portugal has already been bailed out.. (I think.. It seems hard to find out about..) and there is talk of a second one being needed, despite claims for a long time by the Portuguese that it wouldn't be necessary.
One of the reasons Portugal has experienced a worse downturn than most in the global recession is due to the condition in the economy of its main trading parter (Spain). This only goes part-way to explaining the problem, another reason would be the reliance on tourism; the demand for which has fallen sharply in the recession as it is a luxury item that people don't feel they need when their incomes fall.
Spain has yet to be bailed out, despite fears that it may need one in the future, and despite the recent poor economic performance. One of the major fears of the EU is that they probably couldn't afford to bail out an economy as big as Spain's.
The reasons why Spain may require a bailout are not to do with bad governance, more to do with bad luck (as well as over-reliance on certain sectors). It was thought that more than 1/10 Spanish people were employed in the construction sector, and another large proportion were employed in the tourism industry; both of which were hit hard by the recession for the same reasons as Portugal's tourism sector - it's heavily income-elastic.
Also, Portugal's worsening economy is doing Spain no favours.
None yet, and the Italian government are adamant that they will not be needing one.
Italy, like the rest of the PIIGS, is suffering from reduced levels of international competitiveness. It also has a high tourism sector, just like Spain, and the president has freely admitted that the aim of achieving the target of "zero percent deficit and GDP ratio" looks a "long way off"
EDIT: Here's an interesting link I was shown by a friend:
It highlights some of the problems, especially with Greece, and goes into more detail about the bailouts