Is ICMP important?

[Whitley CTR Cecil H]

Hi Chuck,
I would like to point out one fact that you may not be aware of.  ICMP echo
requests and ICMP echo replies are two seperate beasts.  You may have your
firewall set up to allow icmp echo requests and deny icmp echo replies.
This would provide the behavior you are seeing since incoming requests would
not be filtered but incoming replies would be.  Outgoing replies wouldn't be
filtered since your system is generating them.  This would result in others
being able to ping you while you are unable to ping others.

If you need assistance in distinguishing one from the other, let me know and
i'll go look it up and post.  
regards,
Cecil