The Transatlantic Bridge/Tunnel. Would never be built in reality because of the prohibitive startup costs compared to air and water transport, I think. But is it theoretically possible? The Mid-Atlantic Ridge would screw things up, for a start.
Harry Harrison had his characters build a reverse-suspension bridge over the main canyon on the Ridge. I think there were flexible sections with plans to someday lengthen the tunnel.
Considering you've got hundreds of atmospheres outside and vacuum inside the tunnel, one leak and-