If set up correctly, on a decent router that supports it properly, SNMP can be a very powerful tool......as an example (albeit not a good one, since no home-user is going to be using a £750,000 router on an ADSL connection), here's what we're graphing (and monitoring, using another program) on one of our major routers in work:

Main CPU Load
Routing CPU Load
Traffic inbound (on every port)
Traffic outbound (on every port)
Interface errors (on every port)
Packets dropped (SYN and ICMP, on every port)
Flaps (on every port) *a flap is when the interface drops and comes straight back again
Internal temperature using built-in sensors
Number of routes announced (on any port using BGP)

Each graph is set up to update every 5 minutes, and the monitoring system checks each value every 5 minutes against threshold rules configured within itself, and will alert (via audible noise, email, and SMS to the on-call mobile) if any value goes outside of these thresholds.

So yes, configured properly SNMP is a very powerful tool......but, as I said, you'd need to check if the router you're using will actually support it...