All vessel movements are considered public. They are, after all, pretty tough to hide and arrival in port and handling them takes some scheduling and logistics. You can actually look up a lot of ships at
Marinetraffic.com and upload pictures. So, if you see a ship and wonder where it's from and where it's going take a look. You can use the live map feature.
If you are into aircraft, you can do the same thing at
flightaware.com. The link is my local airport but you can use the site to find your own.