It may be worth mentioning that running tomcat as a non root user (which you should be doing) will prevent you from using a port below 1024 on *nix. If you want to use TC as a standalone server -- as its performance no longer requires it to be fronted by Apache or the like -- you'll want to bind to port 80 along with whatever IP address you're specifying.
You can do this by using IPTABLES to redirect port 80 to 8080.