I know that the 74(LS)47 is designed to drive common-anode displays. However, is it possible to make it drive a common-cathode display? What is the simplest (in terms of components) way of doing this?
Yes, it's possible. One method would be to use two extra resistors (plus the usual per-segment resistor) and one PNP transistor per output.
You can buy these three parts integrated into so-called "digital transistors" so it would take only 7 additional parts.
Edit: Re comments by sherrellbc, here is a version for a high-voltage LED digit (something like a 3" digit with multiple LED die per segment) that operates the transistor in the linear region. It provides a constant current of about 15mA for any LED voltage from 0 to more than 10V (it will get warm at 0V).
When it is 'on', the base is at 12V - 2.2V, so the emitter is at about 1.5V below +12 and therefore the collector current will be close to 15mA (since emitter current ~= collector current).
A series of seven 74LS04s on the output.