Graham:Logmein is a remote access solution so not the same as a VPN.
TeamViewer is really cool in my opinion, and has free remote desktop, file transfer, and VPN features for Windows only, but has the same non-commercial thing as hamachi. I've use it and it's solid and a cinch to set up. OpenVPN is complex, but with good instructions for Windows...not at all easy on Linux for me so far. Very capable, however.
NoMachine has several "free forever" clients and uses distributed networking plus "NX" compression technology. Claims to be a really fast "virtual" remote desktop environment for private networks and Internet (http://www.nomachine.com/products.php)....have any of you tried it? With broadband it might be fast enough to make a VPN uneccessary??