Holding more than one citizenship opens up a lot of opportunities for people that happen to be born with multiple citizenships or those who have arranged for a second citizenship.
All countries offer benefits and impose obligations on the countries citizens. Your job is to maximize the benefits and minimize the negative effects of the obligations for each of your citizenships. If you plan well, you can pick and choose benefits to get the best of both citizenships, but if you are not careful you could get the worst of both citizenships. In addition, you may choose to hold residency in a third country where you are not a citizen, which adds to your options and obligations.
Taxes: Consider the tax implications of each country you hold citizenship in. Also you need to be aware of the tax laws of your country of residency (which may be different then your citizenships). Would changing your residency help your tax situation, especially if you are self employed or retired? Can you safely avoid double taxation? Check out tax treaties or get a good accountant that understands multiple citizenship cases.
Military Service: Does one of your citizenships require mandatory military service? In some countries all citizens must serve in the military, which might not suit your personal plans or beliefs. Be careful if you are living in another country and miss the mandatory military service as there can be big penalties that are imposed even years later when you re-enter that country. In other cases, you can safely avoid military service by using your other citizenship to live abroad during the mandatory service window. It depends on the specific laws of the countries involved.
What if your countries go to war with each other? This can create a very difficult situation for a dual national. People get caught in this unfortunate situation during nearly every war. As the world gets more diverse and people increasingly immigrate to other countries, the problem of dual citizenship in wartime will only increase. You could be considered an enemy in your homeland or even jailed as a potential spy. Be prepared if there is a hint of hostilities to solve this problem ASAP.
Education: Some countries offer subsidized or free education to citizens in country. Some rich gulf states even provide full scholarships to study abroad. If you are headed to University, where is the best or perhaps least expensive place to go where you are a citizen while still getting a great education? Would going to your second country for school expose your family to culture, language and opportunity not available in your first country? Can you get a free or inexpensive education in a country you hold citizenship in. For example, Canada is a good option for Americans with dual Canadian citizenship because Canada heavily subsidizes its public universities resulting in low tuition for students compared to similar American universities.
Employment: Different countries experience economic ups and downs on different cycles. If times are tight where you live, does it make sense to relocate to your other country? Maybe jobs in your field are better in the other country.
If you have an EU passport you get the right to live and work anywhere in the expanding EU. This can be a huge advantage.
Certain citizenships can give you easy access to work visas to third countries. For example. currently some citizens of the many Commonwealth countries like Canada, New Zealand, and India can get into the UK for work under one little known program that offers expedited work visas to the UK.
Immigration to a third country: In some cases having citizenship in a former colony can simplify immigration to the parent country. Nationals of some countries are preferred by countries like the US over nationals of other countries. If you want to immigrate somewhere, consider carefully how you will present yourself. Research and ask lots of questions to maximize the employment options.
Health Benefits: Health care quality and cost varies around the world. If you are a Canadian you can benefit from the essentially free health care as long as you are also resident. However, you might be better to go pay for health care in a second country if health care is too costly where you live. If you need extensive health care due to aging or illness you should really look into what benefits each of your citizenships provides.
Retirement Benefits and Pensions: Many people enjoy receiving a pension from another country they are a citizen of because countries like Canada and the Netherlands offer socialized pensions to citizens, even if they resided there only for a short time. Be sure you find out about and apply for every pension you are entitled to have. It might take a little research and may require proving residency, but many years of pension can be very profitable.
Travel: The world is a complex web of interlocking visa and border crossing regulations. Say you want to visit Canada. You can choose between your US passport or another passport that does not offer visa free access to Canada. You would use your US passport because you need no visa that way. It is much easier for a Canadian to travel to North Korea than an American. It is impossible to travel to Israel on a Malaysian passport. There are many similar situations in the world because of various countries have a multitude of relationships with other countries.
In some cases, both of your citizenships may require a visa to go somewhere, but one choice carries a larger fee or offers more restrictive dates. Check out your options carefully and save lots of money on visas.
Personal Safety: Suppose you had been on the Achille Lauro cruise ship when it was hijacked by 1985 by PLO agents. You would be wise to show your Canadian passport not your Israeli passport. Using the right passport in the right place could save your life or smooth your way through a potential crisis.