From Books online:
Permissions
Requires CREATE DATABASE, CREATE ANY DATABASE, or ALTER ANY DATABASE permission.
Since you changed the question...
You GRANT any of the permissions listed above, or give the dbcreator role, which does just about the same thing.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability