The long (and complete) answer is look in the scope (U-1) of the code book (3 pages i length).
The short answer (rule of thumb) is that if it exceeds both of the following, and is not covered by another ASME code, it is most likely within the scope of section VII:
1. Greater than 15 PSI operating pressure.
2. Has in internal diameter, diagonal cross section or height of greater than 6 inches (no limit on length).
There are a ton of exemptions (vessels containing water less than 300 PSI and less than 210F, etc) and some higher pressure limits for small volumes that will not require.
Ulitimately, you the engineer must look over chapter U-1 of ASME Section VII, Div 1 to see if the equipment you are designing falls within the scope.
