Is there a way to monitor all traffic between my computer and a webserver

I am doing some security related project. As a matter of fact, I would like to monitor all traffic between my computer and a certain server. This server may not only send HTTP/HTTPS traffic. Instead there are many many ways that my computer/browser may be interacting with the server. For example, Flash shared objects, sqlite database or index database, or cache files. I tried fiddler. But it seems to give me only HTTP/HTTPS traffic. Is there a way to monitor all the traffic that is between me and the server?? Yes I know I can block some of the functions to stop the traffic. However, I do not want to ban any service. I just want to know what kind of information is exchanging. Thank you for your help in prior.