Are you concerned about the cellular and data charges that may accrue when you travel? These charges can quickly add up and lead to an unfeasibly large bill. When traveling internationally, you can never be absolutely what rates you'll pay. It's often best to avoid these charges entirely.
Turn Off Roaming
All smartphones allow you to turn off roaming on your device. When you're out of your ordinary service networks, your phone will refuse calls and texts; this does not apply to emergency calls. The downside to this, of course, is obvious: you won't be able to get in contact with anyone when you need to. It can be a good solution if you are only going to be out of your service network for a small amount of time. You can also use this option in conjunction with a prepaid phone card so that you can call out, though this won't let anyone call in.
Switch to an International Plan
Call your cell phone provider and ask them if you can switch to an international calling and data plan for the duration of your trip. You can be charged a prorated fee regarding the international plan and switch back to a domestic plan once you get back. This option is ideal for those who want to maintain connectivity with their phone but don't want to have to pay an exorbitant amount; you'll still be paying more than usual, but you will at least know how much you'll be paying.
Use a Prepaid Phone
You can consider getting an international prepaid phone if you are going to be abroad for more than one or two weeks. Prepaid phones operate just like other phones, you simply add credits in the form of minutes to them and you will get a different number. You can use a prepaid phone for the entirety of your trip and simply stop paying for it after the trip is over; a prepaid phone can often be had for less than $20 and is often found in convenience stores. However, don't purchase the prepaid phone domestically; the phones that work on your domestic network may not work internationally.
If you're still worried about possibly ending up with a large bill, you may want to ask your cell phone service provider for their advice.