There are basically two methods for us (consumers) to get internet access without wires: wifi and cellular connections. Wifi is great in the house, at Starbucks, the library, McDonalds, etc., but consumer wifi doesn't go long-distance. For that you need a cellular connection.
You can either buy a device which itself connects to a cellular network (cell phones, of course, but quite a few tablets and laptops can be purchased with this capability as well) or you can create a wifi connection from some cellular devices. Most smartphones can do this (it's called a hotspot), but some cellular providers make this very expensive or severely restrict you, at least in North America.
The story is different in much of the rest of the world. My main experience is in Asia. First of all, if you have T-Mobile as your ISP, you're essentially set for travel. You receive a certain amount of second tier internet in almost all countries for free as part of your plan. After you use up that quota you drop in speeds to third tier, but are not cut off. Calls while roaming are 25¢/minute. I just tested this inadvertently - made a call on my US T-Mobile number to a number in Indonesia. It was indeed 25¢. This is not really a hot-spottable option, because of the speed and quota, but it does work, and if you're only visiting somewhere for a week or two it's totally satisfactory.
What if you're not on T-Mo or need higher speeds? If you have a newer phone it probably accepts eSIMs. If so, there are a number of providers for travel eSIMs. I've used several and had the best success with https://maya.net/ . An eSIM with 5gb of data for Indonesia is $10 for 30 days. Cost per gb goes down with more data or shorter duration. Very easy to set up, and dirt cheap compared to US and Canadian providers (for shame!). They have eSIMs which cover individual countries, groups of countries, all of Asia, and I used one that covered much of Asia, big pieces of Europe, and the US once. It was a lot cheaper than anything I could get from the US providers and worked well in Indonesia, Dubai, Turkey, and the US.
If you're going to be in an Asian country for a while, you should be able to get local cell service without using a travel provider like Maya. For instance, I use Telkomsel here in Indonesia, and receive 25 gb of data which can be shared on up to 6 registered numbers (regular SIM or eSIM from Telkomsel) for under $10/month. If you're just visiting for 6 months or less you don't need to register your phone at customs. If you're here for longer you have to declare your phone with Bea/Cukai (Indonesian Customs) but if the phone isn't new you're likely not to have to pay any duty. Just be prepared with some sort of proof of the value (listings on Craigslist, etc.). And with that you'll have very good cellular internet and be able to hotspot your iPad or whatever.
When I first wrote this I recommended a stand-alone portable hotspot. The one I recommended is no longer available, but there are much better options today. You can buy one here in Indonesia for very little compared to the US ($40 gets you a very decent one) and then can use a Telkomsel SIM card. Most of these don't accept eSIMs, though a few do. I expect that will change in the near future, and I may need to update this post at that time. The first version of this post was written in 2014. A few things have changed since then!
Hope this helps some of you!
