There are many benefits to holding a second citizenship, including increased residential, educational and job opportunities as well as increased ease traveling to or from your countries of citizenship. The United States and Canada both allow for dual citizenship.
The United States does not outright support dual citizenship, but the law does not disallow it. Under United States law, U.S. citizens can hold additional citizenship with any country they qualify for without risk of losing their American citizenship or risk of having to denounce original citizenship upon naturalization as an U.S. citizen. While in the U.S., however, all U.S. dual citizens are recognized singularly as U.S. citizens under the law and cannot claim diplomatic protection from their second nation. Similarly, a U.S. citizen with dual citizenship cannot claim U.S. diplomatic protection while inside of the the country of their second citizenship.
Canada has the same dual-nationality law as the United States does. Canada has recognized dual citizenship since 1977 and, like the United States, does not require the renouncement of any previous citizenship ties in order to become a Canadian citizen through naturalization.
Although the United States and Canada allow their citizens to hold multiple nationalities, it does not imply that all nations do. There are a great many of nations that disallow dual citizenship. Nations that do not support dual citizenship may require the renouncement of former citizenship ties before granting their own citizenship or terminate the ties of their own citizens upon receiving citizenship of a foreign nation.