BARBERINO VAL D’ELSA, TUSCANY— As a kid, I dreamed of traveling. My parents purchased a set of World Book encyclopedias when I was about 4 years old, and for more than a decade that was my conduit to other parts of the globe. I dreamed of far-off exotic lands and what they must be like: the people, the animals, the food. In …

Over the past year, Delhi-based entrepreneur Kavita C has found a friend in Massachusetts. She chats with the 15-year-old schoolboy twice a week, showing him the mango and banana trees that shade her farmhouse and the occasional dancing peacock on her webcam. He turns to her for advice on dinner and to boast about his family vacation to Venice. Theirs …