I largely agree with mathtastic, but I think it is necessary to add something.
When joining a monetary union a country does indeed lose its power to conduct monetary policy. However simply not being able to reduce the interest rate was not the main issue that Greece and other countries faced because of being in the Eurozone. This is because the ECB lowered interest rates (almost) down to the zero lower bound.
To adequately address your question we have to distinguish advantages of a country from having its own currency while in a crisis, vs. advantages from always having had its own currency in the first place.
Reasons why it is helpful to have your own currency when a crisis has already hit:
The issue in this case was the impossibility of devaluation of the currency. One way to understand the Greek crisis is as a current account crisis. Not only was the government over indebted, but the country as a whole. That is to say that there was a too large trade deficit for too long. The trade deficit creates a sort of debt that the whole country owes to other countries in total and was a main point of focus in the debates about Greek debt. You might have heard the issue of competitiveness being cited as a factor in the Greek crisis, which simply means the impossibiliy of the Greek economy to export sufficiently. You may have also heard about "living above their means" or "BMWs going to Greece financed by German money". All this refers to the trade deficit, i.e. the current accuont crisis.
To help itself out of this current account crisis, Greece would have to reduce its trade deficit, i.e export more and import less. If Greece would have had its own currency, a natural reaction to the crisis (without any government intervention even required) would be that Greece's currency loses value. Hence its exports are cheaper which leads to more exports and its imports are more expensive, which leads to less imports. In this way Greece would have an easier time dealing with the crisis and could also "grow its way out of the crisis" - policy advice often heard in this whole debate.
In addition to reducing the trade deficit, a currency devaluation would have helped Greece's economy grow and help with debt service, because the private and public sector were over indebted and not in a position to borrow. This means that domestic demand was very low, so foreign demand- i.e. exports- would have to pick up the slack.
Now, you might say that Greece could export more by simply reducing its prices even without currency devaluation. This is in theory true and is indeed what was recommended and what was attempted in Greece. You can look this up under the term "internal devaluation". However there are several problems with this. First of all it is easier to simply devalue the currency (one price adjustment) than to reduce prices of all export goods (many price adjustments). Furthermore, price decreases mean deflation, which brings with it further problems and is hard to combat later on, when it is no longer desired. A term to look up for more information on this would be "deflationary spiral". Third and perhaps most importantly is the issue of "downward nominal rigidity". This is the empirically observed phenomenon that nominal prices tend to not go down as much as they should or at all, i.e. are rigid in going downwards. This come perhaps from money illusion. It is easier to inflate away workers' wages than to actually reduce them, because the former doesn't cause any protest, while the latter does. Although this is not rational, it happens. Hence it is very difficult to reduce prices and export more (i.e. be more competitive) without an own currency.
This is the reason many countries are likely happy to have their own currency. As to why they are happy despite possibly being "pegged" to the Euro, is because they can break that peg much more easily than Greece if they wanted to.
Reasons why it is helpful to have your own currency before a crisis hits:
For information on how it could have come to such a loss of competitiveness in Greece I can recommend looking up the "Balassa-Samuelson effect", although this may not be the whole story.
Personally, I am not totally convinced by the conventional wisdom, especially popular in European media, that if Greece were to return now to the Drachma that things would be better. This is because their debts may then legally still be denominated in Euro and after the inevitable devaluation of the Drachma against the Euro (the whole point of having the Drachma now) would cause the debt burden to increase even further. For more on models where such effects are present see so-called "third generation currency crisis models".
However had they not had the Euro in the first place, like the "happy" European countries you are mentioning, then their debts would have likely never been denominated in Euro in the first place and could more easily pay that debt through a currency devluation / inflation.
Another reason countries are happy to not have had the Euro in the first place is because the Euro created interest rates for Greece's public debt that were too low than what they should have been. This means the government became over-indebted, which lead to the problems we see today. Had the interest rates been (correctly) higher the government would have perhaps borrowed less and not too much. This is to say that due to the Euro (and the false positie expectations caused by it) the "price signal" was not working so well. Other countries that never adopted the Euro did not experience such a loss of information from the price signal.