Best monitoring software for remote monitoring of servers and network equipment

I am looking for monitoring software that I can use to monitor client's servers and network equipment (routers and switches) from my business location. I would like to monitor things like:

Server - Hardware failure like hard drives and other things, services stopped, etc), running out of storage space, network issues, outages, etc.
Routers and switches - Outages, errors, port utilization to see if there is too much traffic on any port at any given time, etc.

Also, would love to hear how you setup monitoring. I would guess you would open ports in your firewall and your remote locations for the ports used for the software, but don't want to assume.