The cheapest way to stay connected when traveling around the world is to buy a local prepaid SIM card instead of international roaming or using an international SIM card. Depending on the destination you are visiting, you can get tons of data for less than 10 USD, which is much less than the international roaming rates you will pay with roaming.
A local SIM card is a SIM card bought in the destination you are visiting. For example, you can buy a Telstra SIM card, the best operator in Australia, when visiting Australia. You could get a Mobitel SIM card when in Sri Lanka and enjoy fast speeds, or get a Lebara Denmark SIM card when traveling in Denmark.
With a local prepaid SIM card, you can buy packages offered by the local operators, which often have much better deals than international roaming plans. You better stay away from standard roaming rates or Pay As You Go roaming, as that is how travelers come back home and face an expensive roaming bill in the hundreds, thousands, or millions (depending on the currency you use)
If you are visiting multiple destinations in one area, for example, Southeast Asia, then I would recommend reading the sub-continent guides (in this case, the Southeast Asia guide). If you are visiting a single destination, let's say Botswana, then the Botswana-specific guide would be useful to you.
Depending on your source, a country may be considered to be part of one continent (for example Turkey & Russia – both Europe and Asia), while another source will say something else. As a result, a destination may be listed twice on this page, but the information will still be accurate.