The one in particular would be the Altiris Service. However any of those I have outlined could cause errors to be generated, which you'd have to deal with until you got the db back online.

In addition you may want to consider stopping the WWW and IIS Admin services, to stop those errors (clients trying to get to a webpage that is down) from showing up.

If you want to be minimalist in your approach, the Altiris Service and the Support Service (highlighted) are the two key ones. The Altiris service is "the" service, and the Support service will continually try an restart any stopped Altiris services. You should set the Support service to manul or disabled, so it doesn't try and start anything you've stopped.

Don't forget to start SQL on your old box.

At that point, the console should still be pointing to the OLD server location (that way your console will still function). Then navigate to the database setttings location, and change to the new location. Everything will sync up and then you should be all set.

At that point, and at your leisure, you can decommission the second box. The reason why I like this approach is if anything happens during the move, you can always "roll back" to the original install.

JHarrings advice got me on the right track, but for anyone else that isn't already a SQL DBA; here's a step by step of what i had to do on our 7.1 build on Win2008R2 & SQL2008R2:

I was unsuccesful when attempted a direct SQL to SQL copy, so I had to opt for the backup & restore option.

OLD Server: 
Stop all Altiris services, but leave SQL and services untouched.  Open SQL Manager, and login to the (local) server.
Right-click on the Altiris DB  (default is Symantec_CMDB) -> Tasks -> Back up..  Choose Full and choose/make note of the destination folder.

New Server:
Again stop all Altiris services, but leave SQL services running.  Open SQL Manager and right-click on the Databases folder and choose Restore Database. 
Copy the .BAK file created from the old server into the C drive of the new server.
Select to restore from Device: File 
add the copied .BAK file from the old server
Then select the check box next to the DB to confirm which one to restore.
Cross your fingers!

If restore was successful, resume JHarrings instruction:
Start all Altiris services on both servers again
Open the SMC web console -> Settings -> Notification Server -> Database settings:
Change the server name to the new server hostname, select the bullet to use an existing DB.

Depending on your security configuration, you may have to perform this last step on the new server.

All credit to Jim!  Just spelling it out for those of us that learn on the fly.