I wanted to make an easy-to-read topic about GTA 4 and Hamachi, so that everybody out there wanting to play the game over Hamachi doesn't have any problems with it.
HOW TO MAKE GTA 4 USE HAMACHI
To get started we will need to make sure that Hamachi works with GTA 4 and Games For Windows LIVE:

1) Go to START -> RUN...

2) Type in: regedit
and press Enter or click on OK

3) Click on HKEY_CURRENT_USER -> Software -> Classes -> Software -> Microsoft and click on XLive (do not click the "+")

4) Now on your right, right click on the empty background and select:
New -> String Value

5) Name the new value: ConnectionOverride
Press OK

6) Now right click on the new String Value called "ConnectionOverride" and click Modify

7) Type in: Hamachi in the Value field and press OK

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HOW TO CHECK
The steps above will make Games For Windows Live use the Hamachi Network Adapter as the Default connection to play the game online.

So, now start the game using the "LaunchGTAIV.exe"
and make sure Games For Windows Live now uses Hamachi.
You can do this by pressing the "Home" Key, clicking on Personal Settings and then click on Network Information. It should now say "Hamachi (registry overrided)" next to Adapter.

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HOW TO CREATE A GAME
So, now let's continue to get a game going over Hamachi.
in-game press the "up" key to bring out the cellphone and press "Multiplayer"

Create a player model if necessary and then go to "Player Match" -> "LAN" -> "Create Match"
Create a game and make it whatever you like. (ex: Free Mode)

WARNING: THE HOST CAN NOT ALT-TAB OUT OF THE GAME OR THE SERVER WILL CLOSE, KICKING EVERYONE OUT IN THE PROCESS.

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HOW TO JOIN A GAME
To join a game, in-game press the "up" key to bring out the cellphone and press "Multiplayer".
Create a model if necessary and click on "Player Match" -> "LAN" -> "Custom Match" and press F5 to find the servers.

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WARNING: THE SERVER PROBABLY KICKS OUT PEOPLE WHO HAVE A HIGHER PING THEN 25MS SO TRY TO CONNECT TO HAMACHI SERVERS NEAR YOU!

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This should get you going in LAN with your friends.
Although I would want to make one request to those who would like to help these people out.
In order to have people running on 25 or less milliseconds PING, we will need servers for about every country.
If you have a server not yet listed in the posts below then post it!
Some one make a mod to delete the 25ms ping limit in LAN games?? xP