Which Countries allow dual Citizenship and which don't?
Countries that allow dual CITIZENSHIP
In almost all circumstances, yes. You may be required to declare “other allegiances” when applying for certain government programs or a US passport, but their request is more snooping than anything else.
You should be aware that taking up a foreign citizenship with the “intention” of relinquishing your US citizenship can cause you to lose US citizenship. So can fighting in a foreign military or working for a foreign government in any number of jobs.