well there are actually several options:
What I do is have a firewall box which is dedicated and has 2 nic cards so all traffic passes through the box. so its set up like this
Web > modem > firewall > router > lan
Then the 2 nics are bridged so that there is only one as far as the computer knows. Then I can use the box to run tcpdump or whatever logging program I want on that interface. You can then write a simple program and database to log only http traffic and write it to a file or database and have it clean itself out every week or month or whatever. Most firewall distros also have graphical tools in them to monitor traffic and such.
The other way is to have a IDS box and use a tap which is basically 4 rj45 connector set up in such a way that the line is "taped". I don't have one of these but several people on the forum use them.
A third option would be to use a third party firmware like ddwrt or openwrt on a linksys router and use that as your gateway if were talking about a small network. You can run the same tcpdump on one of those and write the file to a desktop computer or some thing.
Hope that helps.