Free Internet Tools to use:

• Robtex DNS: Track down all DNS info related to a site (part of the "Swiss Army Knife Internet Tool")
  
• Robtex AS: View the BGP peering of an AS (part of the "Swiss Army Knife Internet Tool")
• BGPlay: shows animated graphs of routing activity of specific prefixes
• IPCalc: IP Calculator that is great
• HostIP.info: What is your IP address.  (only with out all the mess and spam)
  

Free Monitoring Solutions:

• Cacti: Good SNMP Poller and grapher.  ("nexgen-MRTG")
• Ganglia Monitoring System: Great for collecting enormous data within massive sets of data centers.  Does not do alarming.
• Nagios: Simple standard for host based monitoring and alerting.
• Zabbix: Next step up from Cacti.
• OpenTSDB: Very scalable monitoring platform.  Sounds like Ganglia-ish.
  
• RANSID: simple config collector. 
• SmokePing: a nice pinging tool that graphs and uses rrdb
  

Expensive Solutions to Note:

• appneta: icmp based hosted monitoring solution.  Does not compare to the above, but provides interesting QoS metrics.
  

References:

• SLAC's Network Monitoring Tools: Great list of all monitoring tools out there. (gotta love education jobs, with all that free time :) ... thank god for them!)