Your friend has Hamachi installed as well and is on a Hamachi network with you, right? If not, you need to do this first or else it definitely won't work. If yes, then go into the Hamachi panel and right click his hamachi name and click ping. If it's successful, it will say a time in milliseconds. If it's not, it will say that the ping timed out. Have him do the same thing to you.
If the pings are successful, make sure he's using your hamachi-specific IP number - that's the one that appears on the top of your hamachi window, not the one that registers you to the rest of the internet at large. There should be nothing stopping you if you guys can ping each other, but if the pings are successful and it's still not working, continue along checking everything I mention.
If the pings aren't successful, first off, make sure both of you have rebooted since installing Hamachi. Sometimes the Hamachi virtual driver requires a reboot after installation to be fully functional.
If you're using Windows Vista, 7, or 8, you will also need to make sure the Hamachi network is listed as a home network. If you have a software firewall (Like Windows Firewall or another 3rd Party Product), you need to allow Minecraft through the software firewall some way. Of course, there's the other option, which is simply disabling the software firewall. Your router probably has one (if it didn't why wouldn't you just connect directly to your actual IP address?) so the software firewall is really more of a second safety net - nice, but you don't NEED two all the time. I would try disabling the software firewall, see if he can then connect, and if so then figure out a a way to get it working with the software firewall enabled.
One last option, and this is something I've never tried, but using hamachi as your network may be causing a problem with the normal user verification on Mojang's servers. So if everything else has failed, edit your server.properties file's line that says online-mode=true to online-mode=false - this has nothing to do with whether your server is hosting to the internet, it just stops the game from verifying whether your friend's account is legit or not. And since you're not hosting to the world, only a friend on a cozy little VPN, it's not something to worry about.
