I just use my cell phone number (then they can reach me wherever I am, plus I don't have a home phone anyway), home city, and email. Home city is there because on the off chance they can't reach me an airline may send the bag to Chicago, and I could call the airport lost baggage and get it. I have no idea if that would ever happen, but why not try? So it would say M.Lastname, Chicago, IL, USA, phone, email. Write the phone number as +1 123 456 7890.
If your bag is lost the airline/hotel/whoever will need to get in touch with you. They don't need your address, as they would be unlikely to mail the bag to your home without talking to you first. Once they call you can provide your location or address.. If your bag is lost on the way to Europe your home address isn't useful - you want them to deliver the bag to your hotel in Paris, so once they call you can tell them where you will be.
No one but an airline or MAYBE a luxury hotel would mail a fairly heavy bag across the ocean, unless you pay for it. I'm picturing you leaving it on a subway platform and the subway office calling you. You'd probably just go pick it up there which is why your cell phone is useful.
I agree that having your address is unlikely to cause problems...but I see no reason to take the admittedly small risk so why bother?