International Cell Phone plan or local sim cards?

Bill... I like to keep it simple. Same phone, etc. and I use my iphone all over with the international plan. Still expensive, but I also sign up for the int'l texting plan. It's about $10 for 50 outgoing texts and the incoming are free. So, be sure you don't do any of those one word replies... make the text count. Also, be sure to turn off your data roaming. I don't do a lot of calling, but want to know I am accesible by phone for family. Works great for me.

The answer depends on what you plan to do with the phone. You are right, when you buy a new SIM card you get a new local number. However, this also means that you get the cheapest rates. When you use a SIM from one European country in another, you are roaming; this roaming is not as expensive as roaming from the US on AT&T, but is more expensive than a local SIM from that country. BTW, it's not cities that make a difference for Europe; it's countries. Except for Russia, all the European countries (as far as I know) have nationwide minutes and plans. Another wrinkle: the EU has caps on roaming costs, but since Switzerland is not part of the EU, using a Swiss SIM in an EU country, or using an EU SIM in Switzerland, costs more. If you're just making a few calls, or can make do with texts, it's probably easier to just stay with AT&T. If you're making lots of calls, or need local people to call you, a local SIM will work much better. A compromise would be to get a SIM in your first country, and just use up its value, then get a new local one when the first runs out. If you need data, though, that's a different story. Data roaming from the US can be ruinously expensive, even with one of AT&T's international plans. Some European countries have cheap data plans, but others (even for local use) cost more. And the data roaming rates vary tremendously. Which countries are you visiting, and in what order? For more details (and I mean details), look at this website: http://www.prepaidgsm.net/en/operators.php

Harold We will be saying in this order- 3 nighs in Istanbul, 4 nighs in Rome, 8 nighs in Athens/Greece , 4 nighs Paris and 3 in London before heading home. Lot of different countries in the three week period

If your trip order were reversed, I'd say just get a SIM in London, and keep topping it up on-line. That's because the UK is a very competitive cell phone market, so they have all kinds of specials, and there are often deals for roaming and data. In addition, you can usually get a "free" SIM (e.g. the SIM is 10 GBP, but comes with 10 GBP of credit). Since you're starting in Turkey, you could start with a Turkish SIM (info here: http://www.prepaidgsm.net/en/turkey.html). You'll see that the SIMs are not free. I bought a Turkcell SIM from a reseller (a stand-alone store, because I wasn't near a Turkcell store) and paid 60 Lira for 40 Lira of credit. This is a long way of saying that you won't necessarily get a good deal, particularly for only 3 nights. Another option is to get one of the international SIMs (details here: http://www.prepaidgsm.net/en/international.php. These will work in all your countries. Although these cost more per minute than a national SIM used in its country of origin, they're still less than AT&T's rates, and you don't have to worry about changing SIMs or getting new number with each country. If you search on this forum, you'll see people have posted about some of these international SIM cards. And again, if you plan to use data, check carefully; I believe someone else posted that the international SIM's have high data rates. Do also go to the forums on PrePaidGSM. Although the posts can get VERY technical, the regulars there do know their stuff.

You could check out Brightroam before you leave. They have SIM cards which will work worldwide which you can buy and get in advance of your trip. They also advertise sim cards for iPhones.
www.brightroam.com

This past May, my son was in Costa Rica. Prior to his leaving the country, we both downloaded an App on our IPhone called Viper. It is an app that makes text messages AND calls from/to any country free. My son and I did text back and forth daily, and we talked on the phone a few times. I will say the call had a delay on it, but it worked and I did not get charged anything on my bill for the calls or texts messages. I am travelling to Italy in September and I plan on using VIPER again. This may be an option for you if you have an IPhone. I don't know if it is available on the droids.