I need to check the status of the BRI interfaces from all of the routers on our network. I have to check it everyday to see which one is active. Is there any utility that performs such a task? Do I have to enable SNMP on the routers and would the network performance be affected by this move?
Yes. Any NMS worthy of the description should do this. As an example, I use Zabbix to poll the ifOperStatus of interfaces I'm interested in.
You do not have to, as you could send remote syslog and have your syslog server alert you when it sees an up/down message. However, SNMP is the cross-platform standard way of doing this so will probably be easier.
As for performance, it's impossible to measure something without affecting it, but so long as you're not polling every 5 seconds or something silly like that you shouldn't notice. You can also have a device send an SNMP 'trap' to inform you of the interface changing status.
And finally, for a higher-level overview of how things are working, you can poll the next hop of a particular route with SNMP to see which way traffic is flowing, although this may not apply to your network topology.
I mentioned MRTG, because I'm already using it on some of our routers to check the speed utilization. It would be great if I set it up to include the BRI interfaces as well. Though it will take lots of time and research to setup all those MIBs and OIDs, it would be very interesting. Alerting is not on my plans yet, that's why MRTG would be one of the best solutions.