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Based on most of the rumors (1024x768 screen), etc, they should work. The iPad 2, which is still being sold, is also at that resolution.

Things which may not work, depending on what features are or are not included, are mapping apps (if no GPS like the current Wi-Fi only models). Or, if the app requires a lot of storage, and the mini doesn't support a large enough capacity.

It would seem likely that it will just have smaller screen elements, so if an app assumes a 9.7" screen, it might be too small.

Or, if Apple really goes crazy, and decides to go Intel for the CPU, nothing will work until recompiled.
 
It's one thing to speculate based on rumors, quite another to ask for a prediction as the OP did.

Yes, but how do you expect people to answer technical questions about a product that is nothing but a rumor? Even when scientists speculate they do so based on the concrete facts that they have. There are no concrete facts about the iPad Mini yet as far as I've seen.

I kind of assume when people ask questions in a public forum about a possible unreleased product that it's clear they're asking for speculation based on opinion, extrapolation of current products and known rumors, with the knowledge that all the speculation could turn out to be wrong. If you don't have an assertion to make based on the available information, then why respond just to say no one knows?
 
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