And Doug, if you're looking for a Windows application, the only one I've been able to find is called Pinglog. Sadly, it doesn't do everything you want, and I'm never really sure if I trust Softpedia, but it's something.

I needed such an application in order to troubleshoot connectivity issues in a building-wide network. I left a laptop running that app, and logged into it remotely every once and a while to check in and see how it was doing.

Actually, I had two instances running. One was pinging the router, and the other was pinging anything on the outside, like Google's DNS server (8.8.8.8). That way I could tell if any outage was the result of the internet going down or the network. It worked pretty darn well, though I wish it gave more info than it does.