PICTURE A moment where you're minding your own business when suddenly, out of the corner of your eye, you see someone snatch a purse and start running. Do you chase them down? Legally, you can and if you do, you can make a citizen's arrest, but it's good to know your rights.
In reality, a citizen's arrest isn't as romantic as you probably picture and it comes with a few dangers, including the potential for physical harm and criminal charges against you. It's important to know the rules of when and where you can do it and they vary by country. In the United States, for instance, it's a state statute, so it changes from state to state, with North Carolina being the only state where you cannot make a citizen's arrest. To find out the rules of your state, search the US Government's database of laws.
Lifehacker has a short article that describes when can you make a citizen's arrest and lots more.