I have UK and US dual citizenship (I was born in the UK and married an American, naturalized about a year ago).

Advantages:

• Easier entry into both countries, and countries with appropriate treaties with one or the other. This is somewhat important to me under the current US administration.
• Will allow my wife to get UK citizenship more easily should she want to.
• I can vote in elections in both countries. Also important with the current US administration.

Disadvantages:

• US citizens have to file/pay taxes no matter where in the world they live. I believe the US is the only country that does that - although this does apply to all American citizens, regardless of dual citizenship; I only mention it because dual citizens can more easily move out of the US.
• I need to keep track of two passports, especially when traveling, although I only need to show one at a time.