I agree with vb5prgrmr. Assuming an "Access" scenario, what you really end up with is a Jet database front-ended by one or more VB programs. There's no "Access" to such a case at all, thus no licensing issue. Every 32-bit version of Windows includes a license for the MDAC components you'll need. You just have to deploy them as part of your installation (setup) and excercise a little care regarding versioning.
You don't see many people automating the Access application itself, but I guess I don't know that you can't. I suppose this would be an exception to the above.
If you want SQL Server instead then things get different. As already stated, your users will require SQL Server licenses. An alternative of course is MSDE, a performance-throttled edition of SQL Server minus several management tools. Redistribution licenses for MSDE are implied in several development product licenses. For standalone VB6 I can't find any details, but VS6 Pro and up included MSDE redist rights.
To a certain extent though even MSDE (let alone SQL Server) will complicate things for users unless they have professional support staff. I wouldn't rule it out though.
Even if you develop a VB6/Jet application though, you may want to consider providing functionality to assist users in "compact and repair" and backup/restore operations. If nothing else a separate small program that uses JRO, but note that MDAC 2.5 was the last release that included JRO. Microsoft seems to really want people to move off Jet and onto MSDE, so it might be well worth getting comfortable with.
Sounds like a great book (or article series) topic for somebody: "Transitioning from Jet databases to MSDE for small to medium VB projects." Or is that book out already and I just missed it?