If you are fan of turn based strategy games then Rome Total War must be one of your favorite ones.This game does not offer any problem on LAN so can be played via Hamachi.Here is a simple tutorial to play this game with your friends online using hamachi:
Log onto hamachi.
Now you need to disconnect your internet.There are multiple ways to do this but the simplest one is that you disable your Local Area Connection being used for your internet.This will disconnect you from internet but, do not close the hamachi adapter, leave it as such.
Now launch the game and go to LAN games.
Press Alt+Tab to minimize your game.Enable your internet connection by enabling the disabled Local Area Connection.Hamachi will be reconnected and you now will be able to see all the hosted games through hamachi network.
You can also host the game using this method and your friends can connect you using the same method.