The following steps are the least you'll need to do in order to play most games:
How the metrics and the Hamachi properties should look like in Vista.

1. After installing Hamachi, run it once and insure you've configured your firewall properly and have set port forwarding on your router(s) (if you have one).

2. Re-prioritize your network adapter order:

For XP/2000: Start > Control Panel > Network Connections, then, on the menu bar, click Advanced > Advanced Settings and put Hamachi at the top of the list.

For Vista: Start > Control Panel > Network and Sharing Center, then, on the left side panel, click on 'Manage Network Connections'. Now press Alt, click on Advanced > Advanced Settings and put Hamachi at the top of the list.

For Windows 7: Start > Control Panel > Network and Sharing Center, then, on the left side panel, click on 'Change adapter settings'. Now press Alt, click on Advanced > Advanced Settings and put Hamachi at the top of the list.

3. Configure the gateway and metrics:

In Network Connections right click on Hamachi > Properties, select TCP/IP(v4) > Properties > Advanced. Ensure that the default gateway is 5.0.0.1, if not, then add/edit it and set its metric to Automatic (this is the Gateway Metric).
Below 'Default gateways' tick 'Automatic metric' (this is the Interface Metric).

Quick notice: Some users have reported that their internet connection fails when Hamachi is turned on. Removing the Hamachi gateway (5.0.0.1) should resolve the problem. It is not known why this is happening, but it might be the ISP's fault. Entering a Gateway Metric manually (for example, the default "1500") can restore the internet connection, but gaming functionality may still not be available.

4. If you're running Vista disable TCP/IPv6 (untick it in the Hamachi properties)

5. If you're running Vista ensure that Hamachi appears in the 'Network and Sharing Center' as a 'Private Network' .
If it doesn't, then press customize (at Hamachi, of course) and set it to 'Private Network'.

6. Reboot.

7. Create/Join a Hamachi network and check to see if you can ping/chat with one another. If either one of these don't work ensure you haven't forgotten anything and check again. Still not working? check section 3.1 and 3.2 of the 'Advanced Guide' below.

8. The game host must be running Vista when playing with XP users!