Around Dublin, Dublin
The main thing to keep in mind is pickpockets. They are everywhere in Dublin - especially around the touristy areas. Never put your bags on the ground and do not carry all of your valuables in one bag.
Apparently the trams (Luas) in Dublin are pretty quiet. See photos for info. Although most accidents involving the tram are to do with idiots parking their cars on the tracks.
The day we arrived, the EU was there, so although mugging is very popular as we were told in this city, I felt perfectly safe with the many Gardai.