gistfile1.txt

List<Task> tasks =
[SELECT Id,
       WhatId,
       TypeOf What
           WHEN Account THEN BillingState, BillingCity
       END
  FROM Task
 WHERE WhatId In (SELECT Id
                    FROM Account)];

for (Task t : tasks) {
    // Compiler won't allow this:
    // String billingState = t.What.BillingState

    // Have to indirectly access whatRecord using the get function
    SObject whatRecord = t.What;
    String billingState = (String) whatRecord.get('BillingState');
    system.debug('  whatRecord.BillingState:' + billingState);
}