How can I monitor my home network activity without installing monitoring software in individual pc and macs?

I not sure of anyway you can do it other than using tcpdump and analyzing the logs. But note that tcpdump is on linux/mac.

You could try using tcp dump on mac -> http://tcpdump.darwinports.com/

Additionally, you could request for a web traffic report from your ISP provider.

Hope this helps!

What router do you have connecting your LAN to the internet, it might be something with SNMP in which case you can get something like 'mrtg' and configure it on a mac  to monitor traffic... ( there are loads of SNMP monitoring tools for linux/osx/darwin which do the job, just enable SNMP on your router).

Alternatively you can as askb above has suggested use tcpdump to do it, but that wont specifically give you traffic amounts and usefull figures it will show you actual packet details... is this what you want ?

You need to ensure that your nic is in  promiscuous mode http://en.wikipedia.org/wiki/Promiscuous_mode ensuring that all packets the NIC receives are forwarded through the IP stack. If you are using a switched LAN then you will need to put the port your monitoring from in monitor/observe mode to ensure that ALL packets are forwarded not just those matching the MAC address on the port.

If you give us some more details we can be of more help, but you have left out information on your setup.

Im using a netgear wireless router WGT624. I basically just want to know what my kids have been looking into and how long were they online? I have a serverless home network with a wireless router gateway, a switch and a couple access points.