The reasons why people seek to obtain a second citizenship may differ. Some are looking for greater economic freedom or freedom to travel, settle down and conduct business in certain first world countries, some want to escape the economic and political instability or unrest in their home country or wish to avoid compulsory military service and some simply view the second passport as an insurance of greater personal freedom, escaping from being held hostage by a single country.
You can gain a citizenship of another country either through naturalization or, in some countries, you can buy it. When it comes to naturalization, most countries in the world enable foreign citizens to apply for their citizenship. Some, however, do not allow dual citizenship, so once you have gained the new citizenship you will have to give up on your original one. The factors that make you eligible to apply for a foreign citizenship, apart from being a political refugee, typically include marriage with foreign national, the birth on the country's territory, permanent residence with or without concurrent economic activity in the country where you apply and, in some places, ancestry.
There are countries (e.g. some Latin American countries) where you can apply already after 3 years residing on their territory but in others you can expect having to wait for as long as 12 years (Switzerland). Some countries also have special immigration programs for certain professions. Although in the most countries it is quite easy to apply for a citizenship by oneself, it is advisable to use a specialized law firm that can help you do the paperwork correctly in order to minimize the margin for error. Countries that are generally considered immigration friendly include Australia, Brazil, Canada, New Zealand and Uruguay.
Economic citizenship sounds like a convenient fast track option for gaining a second passport for wealthier people. The prices start from $50.000 onwards per person and they can be paid either in the form of a non-refundable one-off fee or, in most countries, as an investment which will remain in your ownership. Countries that offer economic citizenship programs include Austria, Belgium, Bulgaria, Canada, Dominica, Panama, St. Kitts & Nevis, Switzerland, United Kingdom and the United States. In the commonwealth of Dominica and in Saint Kitts and Nevis the application and the payment of the fee can be arranged during a few days visit to these countries and the new passport will be issued within several months.
In other countries you will have to make an investment in government paper or some selected sectors of the economy and you will be required to reside and conduct business there for at least 3 years before you can apply for their passport. In Panama you can get a passport within a few months if you make a cash deposit in the National Bank of Panama yielding a minimum of $750 per month. Your passport will remain valid as long as you keep this deposit in the bank. Uruguay used to have an immigration and naturalization program for retirees. Under this program pensioners could gain Uruguayan citizenship already after 3-4 months of residing in the country if they invested in the Uruguayan property of government paper. This program is currently being suspended.
As you can see there are a number of options for obtaining a citizenship of another country. If you do your own research you will find many web resources offering help in arranging a second passport. Remember, they can help you do your application correctly but they cannot guarantee you successful approval. It goes without saying that one prerequisite that is common to all economic citizenship programs is a clean criminal record.