If the dropdown menu is a Form Control/ComboBox then its linked cell will contain a value 1,2, etc. In another cell you would use INDEX() to translate the selected value to the text Worksheet1, Worksheet2, etc..
All your formulas would then be:
=INDIRECT(C1&"!A1")
where C1 contains the text Worksheet1 (or Worksheet2, etc.) and A1 is the particular cell's value that you want to retrieve from this sheet.
Note that "A1" is now a string so inserting a row or column into one of these sheets won't cause it to change as it would do normally.
Added: To enable the cell reference to change if rows/cols are inserted in the linked worksheet(s) you would use this version:
=INDIRECT("'"&C1&"'!"&CELL("address",A1))
(courtesy of a colleague, Hans.)