Bringing coins back home from abroad; Is that unethical to do?

There is nothing unethical about keeping your own money. The money you earn is your to spend as you see fit (other than what your government demands you give them in taxes ;-).

Lots of travelers keep their leftover coins and currency as souvenirs, as you mentioned, it brings back fond memories.

Lots of travelers bag up their leftover currency and coins to hold on until they next travel back to that country.

Lots of travelers place their coins in donation boxes or UNICEF envelopes, because they like to help others and have other souvenirs to remind their travels.

Fund raisers will do their best to pull at your heart strings in order to get your donation, but you have to evaluate if their cause is something you want to help. You should not feel guilty simply because you didn't donate.

I once visited a country (I forget which, but it was Spanish-speaking) where there was a shortage of coins for reasons I don't recall. There were signs in many places asking people not to hoard their coins. Of course, that induced me to hoard coins for the duration of our trip. But I made sure to spend most of them before we left, with only a small few for souvenirs. I guess the lesson here is that it depends on the currency. Nobody's going to get burned up by your collection of Euro coins. But in some countries it's a scarce resource, not very nice to remove. And seemingly, you don't care about the value of the coins - so just give them away in the airport on your last day.

Seigniorage,the difference between the value of money and the cost to produce and distribute it, is usually positive. In the US for example:

????????????????????????????????  
?  Coin   ? Cost ? Seigniorage ?  
????????????????????????????????  
? cent    ? 1.7  ? -0.7        ?  
? nickel  ? 8    ? -3          ?  
? dime    ? 3.9  ? 6.1         ?  
? quarter ? 9    ? 16          ?  
????????????????????????????????  

So if a visitor takes home US quarter, he has effectively donated 16¢ to the US government.

Taking home lots of pennies (as we Americans are wont to call our one-cent pieces, using an American pluralization of the name of a British coin) technically costs the government money, but my opinion about the ethics of this is that if a government wants to play stupid games, nobody should feel bad about awarding it stupid prizes.

The question of ethics is generally centered around conflict of interest. An ethical conflict of interest exists when you have an opportunity to do something that will benefit you personally, but will cause problems for a different obligation that exists for you in this context. (For example, a stockbroker who recommends a stock that will earn him a nice commission, but isn't likely to actually benefit the client who purchases it, is behaving unethically by choosing to benefit his own interest at the expense of his professional responsibility to his client.)

If you have an interest in taking money out of a country, but no professional or moral interest in having to leave it there, there's no reason why this should be unethical. However, in some specific cases, depending on the countries involved, doing so could be illegal or subject to legal restrictions, and you definitely have an interest in obeying the law, and an obligation to do so. But in the general case, no, there's no ethical problem with this.

If you're taking money from a country with deflation then you're doing a microscopic piece of harm to the country by removing money from circulation. In a country with hyperinflation you're doing them a very small favour.

By asking "is it ethical", I hope you realize that answers will be primarily opinion-based, so here's a counter opinion:

Some nations (like China, last time I was there) have laws prohibiting removal of currency from their borders. So, if you knowingly and deliberately removed currency from one of these nations, I'd say that it is, in fact, unethical.

Of course, if violating a law is required the fulfill a higher moral obligation, then there is no problem, but I do not consider desiring to have a keepsake a higher moral obligation.