Knowing that we stayed about a month per country and travelled a lot thanks to couchsurfing, the answer came quickly. During my previous trips, I never thought of using an international number. When we arrived in a new country, it was one of our first reflexes and I will certainly continue in my future adventures.
Facilitate couchsurfing and social life
For those who, like us, travel a lot thanks to hospitality networks (Couchsurfing, Trustroots, Warmshower,...) or service exchange networks (Wwoofing, HelpX, Workaway,...), a prepaid international SIM card makes things much easier. Visit
https://www.simoptions.com for more about prepaid SIM cards. A couchsurfer is more inclined to contact his guest on an international number (and vice versa) to accept/refuse a request, to warn of a delay or to propose to go and have a beer in the evening.
Beer brings us to the second point: social life. Well, it's easier (and cheaper) to get organized with the locals for a drink, a story show or a walk in the mountains (all true stories) when you have an international number. On the other hand, we missed several occasions with travellers that we could only contact by internet.
Of course, an international SIM card also makes it possible to call hotels, hostels or tourist places to ask for information at a lower cost.
Having access to the Internet
I hadn't thought about this aspect of things before I left, but having an international SIM card makes Internet access much easier thanks to 3G. In some countries where Wi-Fi is very rare, it was in fact our only access to the web (I think especially of Kenya and Tanzania in our case).
Contact your family and friends
In some countries (such as Cambodia for example), the price plans would have allowed us to contact Belgium or France for much less than using our Belgian cards (in short, without looking for the advantageous Belgian price plans from abroad, it was 3€50 to call from Cambodia to Belgium with a Belgian prepaid card against 0,13$ for the Cambodian prepaid card. But since we had 3G at a very advantageous price and Wi-Fi was quite accessible, we used Skype instead.