A negative of dual citizenship is that you can be subject to obligations such as military service and jury duty in either country.
You may actually be a dual citizen already without you having done anything or even knowing about it. Many countries automatically consider the children of citizens to automatically be a citizen at birth, regardless where they are born. So if your great-grandfather was (say) a Hungarian citizen but moved to the U.S. in the 1920’s, and your grandfather, father and yourself were all born in the U.S. (and never even visited Hungary), you, your father and grandfather would still all be citizens of Hungary.
What, if any, obligations that technically entails you to as a Hungarian citizen (i.e. military) I don’t know. But I don’t believe they have a military draft currently in any event. (Although, like anything, that may change in the future.)