A VPN is a Virtual Private Network. So it is a network (as in, a connection between two or more computers), but it is virtual in the sense that you aren't directly connected to it with a wire.
The only reason to have a VPN is to make your computer part of a network which it couldn't reach physically.
Now, that network can supply you with a new gateway into the internet (even though you're already connecting into that VPN through the internet). So when you use the internet through that gateway, you're basically appearing as if you were physically located inside that VPN. This obviously has several implications. You can appear as being a different location and you can hide your identity to a degree.
I'm assuming this is what you're talking about.
So, setting up a VPN server on your local machine wouldn't do anything for you, because it wouldn't change anything about your setup. For this to make any sense, you would want the VPN server to be a remote machine on a completely different network. The VPN server will just be your gateway into the private network (although it is quite possible that there is no network, just the single gateway computer that acts as both your gateway into the VPN as well as your gateway out of it, into the internet).
So, no, it is not possible to connect to the internet with a VPN without having a server. But you don't need to set up your own VPN server, you can, as you've already noted, just buy or rent a VPN service and use their server.
So, you want to treat a computer as a VPN? I believe hamachi can do this.
– Jon – 2013-08-29T19:10:42.757Your question is non-sensical. A VPN server is an "endpoint" which a VPN client connects to. It is technically possible to set up a VPN server and VPN client on the same machine, but if you are wanting Internet access on this routing will be difficult, to say the least - and whats the point !!! – davidgo – 2013-08-30T06:56:16.867