All in all, I'm pleased with the outcome of our carpet cleaning.  Blackmon Mooring Steamatic came in and did 3 rooms for $99.  Since we did the 3 biggest rooms, I felt pretty good about that. They tout a no-chemical approach (from the Blackmon Mooring site):

Our hot water extraction method uses no chemicals or shampoos for several reasons: shampoos and chemicals leave a residue that actually attracts dirt meaning that your clean carpets will get dirtier faster. The hot water extraction process is recommended by top carpet manufacturers to extend the life of your carpets.

It did pretty well against general grime and dirtyness.  There were some dye-type stains that did not come out, but that's what I expected.  It took longer than advertised for the carpets to dry, so we haven't moved all the furniture back for fear that the wetness would cause more stains around the wood furniture.

The best part was that they showed up on time for the appointment, and finished all three rooms in less than an hour (They advertise 20 minutes per room).  It was very convenient, except for having to move furniture.

I did use it as an opportunity to redo all the connections and such around my entertainment center.  It's much less of a rat's nest now.  I also got the cable hooked back up so I can Tivo something while watching live television, which I disconnected due to a bad coax cable some time ago.  Becky will like that.

[UPDATE] I've gotten several search hits on this, and I wanted to be sure it reflected my long-term opinion.  After a few weeks, most of the stains magically returned.  I imagine that while the cleaning removed the dirt from the stain, that it did not dissolve whatever sticky substance was in the carpet, and it simply grabbed more dirt and the stain re-appeared.  So, one could argue that it removed the stains, but not the cause of the stain.