PortExpert is a free tool which displays all your open network connections, and details about them: protocol, remote address and port, the owning process and its process ID.
You can also see local connections, anything related to your own network. One tap and we could see that iTunes was listening to port 27015 on our test system, for instance, and that something we didn't recognise was using port 5354 (that turned out to be Apple-related, too).
If you'd like to investigate something further, clicking "Search" opens your default browser with the results of a Google search for the process name.
You can also tap "Folder" to open the folder containing the process responsible for this connection.
A "Whois" button tells you who owns a remote IP, and you can just click "Web" to open that address in your browser. Although if you suspect it's somehow connected to a malware infection, that could be a really bad idea.
What you don't get here is any more in-depth analysis of a process, or options to deal with it. There's no double-clicking a process to view its properties, for instance, not even the regular Windows Properties dialog, and you can't kill a connection or process if you think it's harmful.
PortExpert also has no logging or "export" options. You can't save the contents of the list, or even select an item and copy it to the clipboard: the data is strictly for viewing only.