How can I monitor all and any Internet traffic from my home PC?

I would recommend using TCPView which is part of the sysinternals suite. TCPView will show you all of the connections being opened by the TCP/IP stack and it will also show you the remote address of the system it is talking to across the net.

How about Sysinternals TCPView?

"Use NetSpeedMonitor.

NetSpeedMonitor is a lightweight Network Monitoring Toolbar for your
Windows Taskbar designed to be used on computers that run Windows XP,
Windows Server 2003, Windows Vista or Windows 7.

Daily and Monthly Traffic Reports

The amount of data transferred each day, month, and year can be saved
in a SQLite Database. SQLite is the most widely deployed Open Source
SQL database engine in the world and requires not additional setup."

"I see one of your tags is router, so I assume you want to monitor all incoming and outgoing traffic in your network from the router level. If you want to get adventurous, you can check out third-party firmware. If your router can support third-party firmware such as Tomato, it will keep detailed bandwidth usage logs that you can view:

I'm sure the others (DD-WRT, OpenWrt, etc.) also have methods of viewing bandwidth usage."

"If by look at you mean to measure the bandwidth then maybe a program like BitMeter II or BitMeter OS is what you are looking for.

If you actually want to look at the traffic, the a program like WireShark might be what you are looking for."