I think I almost have my iptables setup complete on my CentOS 5.3 system. Here is my script...

# Establish a clean slate
iptables -P INPUT ACCEPT
iptables -P FORWARD ACCEPT
iptables -P OUTPUT ACCEPT
iptables -F # Flush all rules
iptables -X # Delete all chains

# Disable routing. Drop packets if they reach the end of the chain.
iptables -P FORWARD DROP

# Drop all packets with a bad state
iptables -A INPUT -m state --state INVALID -j DROP
# Accept any packets that have something to do with ones we've sent on outbound
iptables -A INPUT -m state --state RELATED,ESTABLISHED -j ACCEPT
# Accept any packets coming or going on localhost (this can be very important)
iptables -A INPUT -i lo -j ACCEPT
# Accept ICMP
iptables -A INPUT -p icmp -j ACCEPT

# Allow ssh
iptables -A INPUT -p tcp --dport 22 -j ACCEPT
# Allow httpd
iptables -A INPUT -p tcp --dport 80 -j ACCEPT
# Allow SSL
iptables -A INPUT -p tcp --dport 443 -j ACCEPT

# Block all other traffic 
iptables -A INPUT -j DROP

For context, this machine is a Virtual Private Server Web app host.

In a previous question, Lee B said that I should "lock down ICMP a bit more." Why not just block it altogether? What would happen if I did that (what bad thing would happen)?

If I need to not block ICMP, how could I go about locking it down more?