I don't know about it being the safest. There are concerns with it since it does call home on a regular basis and no one really knows what those packets contain.
The hamachi server has no way of accessing your system or viewing the packets being transmitted.
The server simply creates the connection between the two computers by comparing the systems public keys to see if they match, it does not actually relay the packets themselves. (Doubt they could offer the service for free if they were forwarding that much data).
My only concern is that its not open source... Other than that it seems fairly robust.
The two programs we use here are BW Phoenix and Hamachi.
Both programs are fairly easy to use so i'm guessing people wont mind which one they use...
They both have their advantages and disadvantages.
BW Phoenix for instance requires port forwarding and all users must install the .net framework 2.0.
Hamachi on the other hand takes a bit more time to set up and become accustomed to, but no ports need opening.