You need to have an international data plan when you travel for navigating around with Google Maps, researching places to eat, posting pictures, and keeping in contact with family and friends.
Sprint offers free texts, free data, and 20 cents per minute calls in over 185 destinations. Plus you can upgrade to even higher data speeds for most destinations for $25 per week, but I have found that the data is fast enough in most countries. I have been a Sprint customer for 15+ years and I have never had any issues when using international data.
Google Fi has very reasonable rates ($10 per GB) for 170+ countries plus $20 per month for unlimited calls and texts. After 6 GB of data in a month, your bill is capped, so a maximum bill of $80 per month. Google Fi now works with most Android and Iphones, but you would need to switch over your phone number.
You can get free texts and free 2G data, and 25 cents per minute calls in 210+ countries. 2G is really slow though, but you can upgrade to high-speed 4G data for $5 per day, however, you are capped at 512 MBs per 24 hour period.
$10 for every day you use your phone outside the U.S. ($5 for Mexico or Canada). Your normal call, text, and data rates apply. You can also do a monthly plan, but it's pretty expensive and only includes a tiny amount of data.
AT&T has an "International Day Pass," which allows you to use call, text, and data plan abroad for $10 per day. However, be sure to turn off your data on days you don't want to use it since background apps could easily trigger the $10 a day fee.
Prepaid SIM Cards
If your phone is "unlocked" you can buy a local SIM card that is loaded with a set amount of data either before you travel or they usually have them in the airport. This option is the cheapest, but the majority of U.S. phones are locked to a specific provider. If your phone is paid in full and your account is in good standing, you can request that your provider unlock your phone. You can find these forms online: AT&T, Sprint, Verizon, and T-Mobile.
You can also rent a portable hotspot and connect you and travel companions' phones to the WiFi network. I have a SkyRoam, which you can rent from their company for $9.95 per day (including the daily WiFi) or buy the hotspot for $149 and pay $9 per day or $99 per month (or sign up for their monthly plan that offers 1 Gigabit for $9 per month and additional GBs are only $9 per GB). There is usually a 15-20% off code for buying the hotspot if you Google around. The big advantage of the SkyRoam is that you can connect up to five devices at once, rather than pay Verizon or ATT $10 per phone ($50 per day for five people). The WiFi is unlimited, but I have read reviews that data is throttled after 5 GBs per day, but that's a lot of data to use in a single day.