Hi BP,
I'll give you an example of how I'm using it.
Right now, my home connection to the internet is via a wireless provider, who gives out private (Intranet) IP addresses.
So I can not reach my home from the Internet, because lack of a public IP (it sits behind their NAT firewall).
But
Never fear, because the tricks are here 
As you know, I have an "Asterisk" PBX at home ( Asterisk@Home), and I no longer have "Ma Bell" phone company services

So I can call out without any problems, but nobody could call me, because of the problem of the private IP address.
Well, I just connected via an Asterisk IAX2 trunk from my box, to "Free World Dialup" (FWD), and then forwarded a free IPKall.com land line to my FWD number.
So now I can receive calls from anyone in the world, even though I'm behind a firewall

But now, back to the real case and question, which is accesing my home machine from the Internet.
That's where the Yellow Tuna (Hamachi) comes in

In the same machine I'm running at home for Asterisk, which is a CentOS Linux distribution BTW, I installed Hamachi Linux software.
So now, I can be anywhere in the world and I can connect with my Windows notebook using the Hamachi Windows software, and I connect to a group I created at home.
So basically I can now see my shared drives, and I can even run a SIP client on my notebook, using SIP protocol, and it works perfectly fine because I don't have to punch any firewall holes

It's truly amazing the way it works, just like the audio file you listened, and with comments like that coming from Leo Laporte (TechTV) and Steve Gibson (Gibson Research), you can be assured it's really a secure product
Edit: As for your VNC question, for sure

go ahead and use it

Just install Hamachi at all your clients, and then instead of connecting your VNC client in the wild ( public_address

ort ) you would just connect to your customer's

Hamachi_IP_address

ort and that's it

Now all your VNC communication is encrypted via Hamachi point-to-point VPN

Just think of all the neat things you can do with this
EDIT #2: BTW, here are some great "NAT Router Security Solutions"
http://www.grc.com/nat/nat.htm
-kwag