You can do remote assistance to XP computers for free. It's built right into XP. It integrates with both Outlook and Messenger, and the user can initiate the request, or you can send a request to the user. It works pretty well.
I uninstalled LogMeIn once I discovered the free Remote Desktop features built into Live Mesh. Works very well and as far as I can tell it works whether the client is behind a NAT router/firewall or not.
Does it require the person on the other end that needs your support to have an MSN account?
The person on the other end just needs to have Live Mesh installed and setup with one account, so I guess the answer to your question is no.
For example, I have a Live.com/Hotmail/MSN account that works with all Microsoft products/services. I use that to login to my Live Mesh account and install the client on all the machines I want control over.
In a way, its exactly like LogMeIn.