Avoiding excessive charges is one key trick for International Travel with an iPhone. International travel can include a quick cruise to Mexico or the Caribbean, or a full-on international flight. Either way, some tips I've learned will save you money. I spent a week in Singapore and saved $60 over what the roaming rates would have totaled for data, SMS and calls.

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Service Add-ons:
Use AT&T myWireless Mobile app to activate/deactivate additional services rather than calling AT&T. I recommend doing this at least 72 hours before you leave the USA.
Tip: When you activate the add-ons, immediately set an appointment or “To Do” to de-activate 10 days after you return. You'll save a few dollars that month since it is pro-rated, and won't accidentally carry-over the service into future months.

If you need to call or just prefer it, note that you'll need to make 2 calls. First call the regular service number (611 on mobile or 800-331-0500 from another phone). Second, call International Wireless Care at 800-335-4685 or if already abroad, +1-916-843-4685 to add your “Data Global Add-On” for International Data. Do this AT LEAST 72 hours before you leave; it can take 24 hours or more to activate.
Tip: Add “AT&T International” as a Contact with the 916 number above. You can quickly call for support or to update service.

AT&T World Traveler” is just $5.99 a month and is pro-rated. It can save you $0.30 to $1.00 per minute on calls you receive (rates here). The cost of each SMS message can drop a similar amount. The gotcha is be sure to leave it active for ~10 days after your return. If there are delays in international billing you'll get hit with the higher rate if you already de-activated this add-on.

Regarding the “International Roaming- Data”- Pick a plan that suits your needs. I watch my data budget tightly and did fine with 20MB ($24.99) for a 6 day trip. I turn off “Data roaming” often and use WiFi where I can. I was ready to call and upgrade if needed though.
Tip: Before you travel, reset the iPhone Usage and watch it for a 2 days to see what your data budget might need to be.

Skype:
Buy in US dollars before you go (or stay in euros if your account is already in euros). Don't switch currencies on your Skype account; you'll get hit with a currency conversion charge. I started on Skype years ago when Euros were the only option. I'll only switch to US Dollars when my account is at zero.

WiFi:
72 hours before leaving the USA, Scout for WiFi. Check with the hotel or conference venue to see if WiFi is available. That can greatly reduce 3G data needs. It will also help you decide how large of a data plan to buy.
Tip: Check if the hotel has a frequent guest plan, many hotels offer free or reduced WiFi for frequent guests. Sign-up before you leave the US.

Data Misers:
Set a recurring alarm for “data off” (bedtime) and one for “data on” (wake). Toggle the Data Roaming setting accordingly. You can still get calls or use alarms, but won't be disturbed (or charged) for night-time email updates. Get them in a batch at a WiFi spot or when you turn on 3G data again.

Preload maps by searching for directions while at a WiFi spot. You can still get updates via 3G while out and about, but the larger map will already be downloaded.

SMS:
48 hours before leaving the USA, turn off or dial-back on SMS updates. Why 2 days before leaving? So you can catch that one extra service you forgot. Likely sources of SMS reminders to turn off are: Google Calendar, Jott, Remember the Milk, TripIt Premium, twitter.
Tip: Once you've established your new locale, do more than set the iPhone time zone. Also set your twitter time zone preferences to reflect your “do not disturb” hours for the new time zone.

Don't be surprised if you receive 1-2 SMS messages from AT&T as you travel. AT&T will alert you when you're in a roaming zone and you are not charged for those messages.