Some people recommend that this be done periodically to heighten security, and in some senses they are correct. It is much more difficult for someone to hack into the machine from the outside if the admin account name changes. However, there's little or no real heightened security if the machine is hacked from within via a trojan or some other form of subterfuge.
In Windows NT/2000/XP, the user's name is actually not as important as the GUID, or globally unique identifier, that is generated for the user account. The GUID is what is used to track permissions and security for an account and not the name per se.
On the server I administer, I periodically change the username and password for the admin account. However, when I do this, I have to manually reset any of the batch jobs that are run with that account name -- such as the automated jobs that run in SQL Server with admin permissions (which are required to perform certain tasks). Bear this in mind if you change the admin account name and suddenly things don't work like they used to -- you may need to re-initialize how the names are handled since they don't synchronize automatically in third-party apps.
This was first published in March 2002