Or stop the SQL services and COPY the .mdf, .ndf and .ldf files, leaving the originals intact on the source server, and then sp_attach_db on the new server. I don't necessarily agree that a backup/restore is any safer but I do agree with jhocutt about backing up the databases - PRIOR to doing anything.
The reason why backup/restore is safer is because you haven't modified the source database. When you use the detach/attach method, you are modifying the source database. What happens if you can't attach it back? With backup/restore, you don't have that risk.