Multi-user Access apps are pretty easy to do for small workgroup user populations in the 15-25 ranger or smaller. Above that, a developer should consider upsizing to a server back end, with the trade-off being greater administrative overhead for the server vs. having to program the app more carefully if you retain the Jet/ACE back end.
As to online access, you this isn't possible over HTTP, but if you have a Windows Terminal Server available, you can host your app there and give users access to that. This is actually an extremely easy and efficient and inexpensive way to support remote users of an app, though the larger the user population, the more problematic it becomes. But by the time an Access app has a user population that would strain a Windows Terminal Server setup, you're no longer going to be using a Jet/ACE back end.
And with a server back end, you could give access to a SQL Server on a VPN over the Internet, and if you write your Access app really efficiently, even over a standard broadband connection, your users could still work productively.
Then there's the future of Access: in Access 2010, a great deal of work has been done to integrate with a host of new features in Sharepoint 2010. If you create your A2010 app using the new type of Access web forms and reports, your app can be uploaded to a Sharepoint server running the new Access Services, and it can then be used running in a web browser (not limited to IE and not dependent on any plugins or web controls, as was the case in the past with the completely worthless Access Data Access Pages). The data store can either be a SQL Server, or you could keep it Jet/ACE for users not accessing it via the web browser, and have the data stored in Sharepoint for the online users. Also, you can have an app integrated with Sharepoint running locally in Access that uses Sharepoint when connected to the Internet, and still be able to work offline when disconnected. When connected again, you synch your local changes with the Sharepoint server, resolve any differences and continue working.
The features are really quite remarkable, and according to what I've heard and seen, if the Access app is built entirely of web forms and reports, it will look and function identically when run in Access and when run in the web browser via Sharepoint. And if you need to have client-side features that you don't expose to the users running the app in the browser, you can still use traditional Access objects!
The Access development team's blog has a number of posts on what's coming in A2010, and there's a good video posted there demonstrating how A2010 integrates with Sharepoint 2010's new Access Services.
This constitutes a quantum leap in Access's web capabilities, which were previously almost non-existent, and I'm quite excited about this. I was formerly quite wary of the changes being made to Access that seemed entirely to make it a servant of Sharepoint, but now I can see that the benefit to Access users and Access developers will be huge.