I have an earlier post on the subject, but thought I'd expand a bit:
I'll say the less positive stuff first: Unless one's iPhone is unlocked, the AT&T $6/month World Traveler plan, which drops per-minute charges a bit, is an iPhone owner's only option for over-the-phone communication.
Unlocking happens through a hack, as described in this Wired article. Unlocking and jailbreaking — alowing non-Apple-sanctioned apps — are doable and ultimately not that hard, but we recommend against these hacks on phones that are still in use as primary phones (as opposed to being sold or converted to an iPod touch).
Now, AT&T has some good recommendations for travelling overseas with your iPhone, including something I just found out, and wish I had known for my South America trip last year: their Data Global plan. This might come in handy; there was a lot of travel research I wanted to do on the fly.
But my bestest tip for people travelling internationally with their iPhones is still Wi-Fi! It's so awesome to have a great, little internet device in one's pocket. Whenever I'm travelling, and have a moment or a need, I scan for free wireless. Café-sitting is one of my favorite touring activities, anyway. I was happy enough with this for email and chat, but now you can make free iPhone-to-computer voice calls with the Skype app [iTunes link], and supposedly one-way video chat with Fring [iTunes link].
If you don't get the World Traveler plan, do read those AT&T instructions for turning off roaming, or you can wind up with a huge bill. Even if you do buy the plan, it turns out that you get charged for any incoming calls, whether you answer them or not(!), and voicemails, even if you don't listen to them.
My technique was to leave the iPhone in "Airplane Mode," and then turn on only Wi-Fi and scanned for open networks when I needed one. I had no surprises when I came home.