What is a good example (or examples) of a "service without a statement of work"? I'm unable to locate a clear definition other than "where a statement of work is not required (e.g., installation, maintenance, and repair)" as shown in FAR Part 8.
Good question; I'm assuming you are trying to determine if FAR 8.405-1 applies to your procurement action.
The FAR (nor your Agency Supplement - the VAAR) provides a definition for supplies or services that don't require a statement of work (or PWS). In that case the common dictionary definition applies. So basically it is a scenario where what you are buying is simple and straightforward enough that industy knows exactly how to produce/package/deliver the item or accomplish the service tasks without being told how to do it, or what specifications it must meet, or any special requirements you may have that industry would be unaware of. An example would be you are buying an item with a national stock item number (NSN) and the NSN is enough of a description for industry or prospective offerors to know.
If you are still unsure, you may be better served by reading FAR Part 11 - Describing Agency Needs, and also FAR 37.602 if you are buying services. You'll want to review the corresponding guidance in the VAAR as well. If you need help with services, a great resource is the Services Acquisition Mall at: https://www.dau.edu/tools/Documents/SAM/home.html