In a previous post, I've described how you could generate a (almost) continuous ping from a router using the extended ping command. While that approach is extremely simple to implement, it ties up a line (and if you're working from the console, it's highly impractical). You could get the same results (as Tom has already pointed out) using IP SLA feature of Cisco IOS. Configure the ping request with commands similar to these:

ip sla 100
  icmp-echo 172.16.1.2
  timeout 500
  frequency 3

To start the ping, use the ip sla schedule 100 life forever start-time now configuration command, to stop it, no ip sla schedule 100 command. When using IP SLA ping, you can trigger Embedded Event Manager applets to report ping failure (similar to the technique described in this post) or read the ping results from SLA MIB with SNMP.

Note: In IOS release 12.3(14)T, the ip sla command replaced the rtr command. To use this technique in IOS release 12.3 or lower, use the rtr configuration command.