Who is this 'Anonymous' user??

Windows NT networks based on a single Windows NT domain will always be able to authenticate connections to list domain account information. Windows NT networks that use multiple domains may require anonymous user logon to list account information. A brief example shows how anonymous connections are used. Consider two Windows NT domains, an account domain and a resource domain. The resource domain has a one-way trust relationship with the account domain. That is, the resource domain "trusts" the account domain, but the account domain does not trust the resource domain. Users from the account domain can authenticate and access resources in the resource domain based on the one-way trust. Suppose an administrator in the resource domain wants to grant access to a file to a user from the account domain. They will want to obtain the list of users and groups from the account domain to select a user/group to grant access rights. Since the account domain does not trust the resource domain, the administrator request to obtain the list of users and groups from the resource domain cannot be authenticated. The connection is made using a NULL session to obtain the list of account domain users.

Now the question is, do you have multiple domains or users who are reaching your domain from say a workstation that is in a workgroup or the Internet?

You can disallow anonymous connections with a registry modification:
Run Registry Editor (Regedt32.exe).
Go to the following key in the registry:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\LSA
On the Edit menu, click Add Value and use the following entry:
Value Name: RestrictAnonymous
Data Type: REG_DWORD
Value: 1

Once you do this, all users will be forced to authenticate to your domain controller before being granted access to resources.

If you have IIS runing on your server and are hosting a website, You'll have a anonymous user set up for those connections from the internet which are allowed to browse your webpage. Make sure that anonymous user doesn't have any write access to files on your server. If you ho to the web directory you should be able to see who has what kind of access. Also have a look at your IIS manager.

If I remember correctly, IIS is installed automatically on an NT Server. If you don't need it, disable or uninstall it (also check any FTP Service you may be running).

Do you have trusts setup to another domain? I think this is what shows up when a user authenticated by another domain accesses resources in your domain.