I'll be traveling across South America for a month. I'd like to buy a local-ish prepaid sim card upon arrival that I could use for local calls and casual internet access using my smartphone. I have a European unlocked phone, so no problem about that. Specifically, I'll first arrive in Ecuador, then continue to Peru, Bolivia and finally Chile for the last couple of days. It would be great to buy the card in Ecuador and use it throughout the journey instead of buying one at each place. The main criteria would be that I'd like to be able to receive calls and SMS for free, make some local calls for simple travel arrangements and have access to internet time to time for emails or looking for basic information. Is that possible, or is the only way to avoid hefty charges from my European provider to buy a separate sim card in every country?
On top of that, South American cellphone networks tend to be somewhat fractured, meaning that out-of-the-way locations might only be served by one, or a few, of the nation's networks.
So, with a foreign sim card, you might be able to use multiple local networks, but, indeed, at a cost.
If you expect to use your phone extensively, your best bet is to get a local sim card. However, also keep in mind that some countries will require you to register the card with the equivalent of a local social security number. (I don't know whether Ecuador, Peru, Chile or Bolivia need this, but Brazil most certainly does.)
But, some personal experience, I spent quite a few months traveling around South America last year and this year, I never really missed not having a local number. Wifi access is almost ubiquitous. And in places where it isn't, cellphone access tends to be an issue as well.