In Windows, if you're curious about your system's network connections, a quick trip to "netstat" via the command-line will usually sort you out. But if you're only interested in TCP activity and would prefer a user interface and running log, you need to check out NirSoft's TcpLogView.
NirSoft has been a repository of useful freeware Windows utilities for a long time and TcpLogView is just another excellent feather in the developer's burgeoning cap. At just over 150KB and no need for installation, it's the perfect, portable tool for quickly inspecting one of the most common types of network activity.
The user-interface can be viewed in the image above and yes, it's as straightforward as it looks. The log will keep track of connections as they open and close, reporting the process responsible along with other details including the remote IP address and port.
Netstat, of course, also shows network activity via other protocols such as UDP, but for the majority of connections, TcpLogView should have you covered.