why don't you be a touch more spesific.... what OS ? and do you want to monitor all your lan traffic ? or maybe you mean to filter for just traffic going to the web ? or your whole network ?
/me take a guess
In windows, to monitor total network traffic (no filtering for destination) , DUmeter works nice.
monitoring the traffic on the internet would be quite difficult. downloading the internet might be easier
but you might want to check out TechTv's screen saver website. I remember that one guy... umm.. The Dark Tipper? Kevin something. He showed a program that monitored network traffic, et cetera.
I'll be hunting it down eventually and using it for when I have a larger then normal LAN. so as to make sure my bandwidth isn't being used for stupid things.
Something as simple as MS network monitor or ethereal will give you what you want if you set up the capture filters appropriately. Just make sure you dont set up behind a switch.
Lets see.... you want to monitor your personal networks usage to the internet ? Why don't you just setup your routing computer to do such ?
To do it on a 3rd computer that isn't filtering/forwarding packets is not going to be an easy task. I would think you would need to capture all the traffic (so you can't use switches), then inturprat it somehow. Sure, you could do it... but using a computer to forward is going to make such a task many times easier.