To expand on the "cellular" part of the equation, I use a device from Skyroam (no affiliation) which basically gets a virtual local sim for you. It's not cheap if you want a lot of data, but it's great for checking your email and generally staying connected. Unlike a sim solution, you don't have to find out where to get a sim card, put the sim card into your phone, type long strings of numbers etc, manage old cards that might use again, and so on. You just power it on and connect to it as a wifi hotspot. Also you pay the Skyroam people so you don't need to investigate which local provider offers the better deal. If a place has cell service, the Skyroam works. It even works in Singapore, where all cell phones are connected to identity and tourists have to show their passports (and the number is recorded) to activate a temporary sim. I've used it on trains and in the back of cabs and at campsites -- all places where wifi is pretty unlikely.
Note: it does not get you a phone number. Services like texting that rely on a phone number won't work. It gets you a wifi hotspot.
I am not going to link to it because I don't want to spam.
The Americas: Anguilla, Antigua & Barbuda, Argentina, Aruba, Bahamas, Barbados, Belize, Bermuda, Bolivia, Bonaire, Brazil, British
Virgin Islands, Canada, Cayman Islands, Chile, Colombia, Costa Rica,
Curacao, Dominica, Dominican Republic, Ecuador, El Salvador, Grenada,
Guadeloupe, Guatemala, Guyana, Haiti, Honduras, Jamaica, Martinique,
Mexico, Montserrat, Nicaragua, Panama, Peru, Puerto Rico, Saipan, St.
Kitts & Nevis, St. Lucia, St. Marteen, St. Vincent, St. Vincent & the
Grenadines, Suriname, Trinidad & Tobago, Turks & Caicos Island, United
States, Uruguay, Venezuela
Europe: Albania, Austria, Belarus, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany,
Greece, Hungary, Iceland, Ireland, Italy, Latvia, Liechtenstein,
Lithuania, Luxembourg, Malta, Monaco, Montenegro, Netherlands, Norway,
Poland, Portugal, Romania, Russia, San Marino, Serbia, Slovakia,
Slovenia, Spain, Sweden, Switzerland, Ukraine, United Kingdom, Vatican
Asia: Bangladesh, Brunei, Cambodia, China, Hong Kong, India, Indonesia, Japan, Kazakhstan, Kyrgyzstan, Laos, Macao, Malaysia,
Myanmar, Nepal, Philippines, Singapore, South Korea, Sri Lanka,
Taiwan, Tajikistan, Thailand, Uzbekistan, Vietnam
South Pacific: Australia, Christmas Island, Fiji, Guam, New Zealand
Africa: Egypt, Kenya, Madagascar, Mauritius, Morocco, Nigeria, South Africa, Tanzania, Tunisia, Zambia
Middle East: Bahrain, Dubai, Iraq, Israel, Jordan, Kuwait, Oman, Qatar, Saudi Arabia, Turkey