Update the parts whenever needed without the user even noticing.
Not all software are webapps (though I agree versioning is much less important, particularly for the end user, in those cases).
For those of us writing enterprise software that gets installed/ran by customers versioning is pretty important:
* Unlike a website not all our customers are using the same version, so when a bug is reported we need to know what version it was encountered.
* Customers need to know if version X of product A is compatible with version Y of product B.
* Gives customers an idea of the magnitude of changes, e.g. bumping the minor version will usually indicate mostly bug fixes, security updates, and small/non-API-breaking features.
* Facilitates easier communication with QA, beta testers, etc than referring (only) to a build.
Webapps/SAAS applications are clearly different because customers don't install anything and therefore version numbering from a customer perspective does not have any meaning. Therefore, any meaning we attach, is for internal internal consumption only.
In even in that case, I would argue that version numbering is important. E.g the point on easier communication is exactly where internal consumption requires version numbering.
As a user, I especially want software versions to know what I'm using.
I hate it how Facebook pretends that some features are bugs (for example - switching from most recent to top stories in my news feed) and I want to be able to report this, but I'm kept in the dark in regards to versions, changelog, basically everything except the UI.