Not possible. Why?
Well in a way what you can do is set up layers with sublayers for each artboard and then when viewing the artboard lock the others and save that as a view. View>New View you can also make the layers and collect them in another layer and then lock the collected layers not associated with that layer and if you have that artboard selected to fit page to window you will return to each artboard at that magnification.
Like such exactly what you want but it could work for you.
Incidently, that's a change recently made to Corel Draw (X4). It was reportedly done in response to user requests. In the feedback I've read, though, it doesn't seem to be very popular. I haven't played with it enough yet to really judge, but I can see how it can be confusing. I'm not convinced it's really advantageous.
I would think it would make the use of multiple art boards a little difficult to work with as you can now easily drag copy art from one board to another and things like that.
And if you update a symbol like a logo you might want t see how all of that looks and effects each artboard.
But there could be an advantage as well.
I do not know the feature that Corel has but I always think it is best to really consider all the possibilities good and bad before finalizing a feature.
No, not possible andm, as James (JET) said, not really sensible, given how AI generalises on using elements across all artboards. Designing multifold print products with seamless graphics would be infinitely more difficult as would be a number of other things perhaps one day when AI's artborads have options for master pages/ templates it will begin to make sense in a differential way (only the content that is doiffernt on each page is shown as a per artboard layer stack), but until then for the majority of tasks it does not seem to be a desirable feature.