Multiple Tray Ping (Freeware) by Moxim Software
One of my neighbors runs a node SSID www.personaltelco.net, leaves his AP on, but not his gateway server. (Don't ask me why.) This program pings his gateway server periodically and shows the status of the last ping as a red or green light icon, and I drop by dialup connection and use his. It works very well.
IP Ultra Scan 2000 (Freeware) by Ultrajones Software
Is an IP ping scanner and port scanner. I haven't used the port scanning, for golden rule type reasons (and I wouldn't know what to do if I found them.)