I've encountered parents that purchased the web domain name for their child's name when s/he was born. This way, no cybersquatter can show up and take it. But other parents go ahead and create full social networking profiles for their children:
Link via Buzzfeed | Photo by Flickr user Iragerich used under Creative Commons license
According to a recent international survey of 2,200 mothers, 81% of children under the age of two currently have some form of online presence — ranging from photos uploaded and shared by their parents, to a full-fledged profile on a social networking site. A full 92% of children in the U.S. have an online presence by the time they are two, compared to 73% in western Europe.
Link via Buzzfeed | Photo by Flickr user Iragerich used under Creative Commons license