For our recent trip Ken and I took our iPhones. It's nice to stay in touch back home and I've become pretty reliant on my iPhone for getting around. Here's some tips on using an iPhone internationally for Americans stuck with AT&T. (There's a whole alternative of unlocking the phone and using a European SIM; not discussed here). See also AT&T's iPhone travel tips, they're pretty useful.
AT&T's roaming is pretty unreliable. Half the incoming phone calls I know about never arrived, not even to voicemail. Caller ID doesn't work. SMS messages disappear. Rates are outrageous, something like $2/minute. It's a bit cheaper if you set up "AT&T World Connect" on your account for $4/month before you leave. But who cares about the phone, you really want your iPhone as an Internet terminal. And it works pretty well for that in Europe, provided you either find free WiFi or else you don't mind paying through the nose.
If you don't buy the "Data Global Add-On" you will be paying $10/mb for data from the cell network (EDGE or 3G). That's absolutely hideous pricing. You can pre-order a chunk of 20, 50, 100, or 200 mb/month at roughly $1 / megabyte. That's still outrageous but bearable. Note: you can order the data for just a few weeks and cancel. Overage is $5/mb.
How much bandwidth do you need? If I was being careful, it was 2 mb/day. That was enough bandwidth to catch up on email and Twitter twice a day, maybe get a couple of web pages or upload a photo. Then I had one bad day where I looked up a few maps and restaurants and blew through 10 megabytes. You really have to be careful.
How do you be careful? #1 way is to find free WiFi. There's a lot of free WiFi in Europe, more-so than the US. Public town squares, train stations, and busy cafes are good bets. Sometimes the cafe WiFi is password protected, just ask and they'll give you a password. Hotels are hit and miss. A lot of my rooms only had wired Internet, I regretted not bringing a little WiFi router.
If you're stuck with using cell for data, the #1 option for being careful is to turn off "Data Roaming" in Settings. If you do that, you'll use no bandwidth. You'll also not be able to use the Internet. Geolocation won't work well either. I found it really irritating to have Data Roaming off all the time. So instead I configured the phone to be lean by turning off Notifications and "Mail / Fetch New Data" in Settings. I also reset my Usage counters to track what I was using in Europe.
iPhone apps will still use a lot of bandwidth when you launch them. The real killer is Google Maps, a total hog. OffMaps is a nice alternative with cached maps in offline mode. Expect to pre-load 500-1000mb of maps for a long trip, you really want the finest grain detail when walking around. Apple's Mail app is reasonably network efficient, particularly compared to Gmail in Safari. The New York Times app is great for caching a bunch of news articles on WiFi then reading them later. And Twitter is a great low bandwidth way to keep in touch with people, although apps like Tweetie are not particularly network efficient.
AT&T's data roaming charges are ridiculous and it's a real pain watching your bandwidth. But it's totally worth it, the iPhone makes a great little companion while travelling. I particularly liked being able to use Twitter as a travel diary complete with photos, it was a lot of fun seeing responses from people to what I was doing that day.