Ya this is needed in many such occasion - like Proxy white-listing / Getting access through 3rd party Firewall / troubleshooting anything on web server specific to your request etc.
On linux Command prompt I would do somethign like this :
[root@DebaTestBox ~]# wget -O - -q icanhazip.com
[root@DebaTestBox ~]# curl ifconfig.me/ip
Eventhough there are many such sites(most of them are flooded with ads!!) - who gives your Outgoing NAT public IP info - I know some lighter once -
Woindows users can simply type any of these above URL in the browser - not sure - if we can use any cmd like you can do in *NIX console.
PS: Please add to the list if you know more secured one's