What would it mean if every continent of the World was interconnected by floating bridges or tunnels?

How much would a connection between the US and Europe, for example, reduce in terms of shipping times, personal travel times and costs?

The thing I find most appealing in this idea is the fact that such a connection would change the World, forever. It would probably take a century or so to finish, but every man, women and child born after this would open their eyes to a World integrated without precedent.