I'm not sure how many people out there are as sensitive to the fragrances found in most carpet-cleaning solutions as I am, but I was happy to discover recently that you can easily find alternatives by doing a simple internet search.
The two I was happiest to find were one article on using baking soda, and another on using hydrogen peroxide. I've used baking soda before and was pretty happy with it, but I'm always glad to get more instruction. Baking Soda is included in this link: Clean Carpets without Dangerous Chemicals.
I am a little wary of the "sprinkle on, vacuum off" method, though, so finding out from a friend recently that you can use Hydrogen Peroxide sounded great. This one, "Using Hydrogen Peroxide," mentions combining Hydrogen Peroxide with simple Castille Soap, but I watched a friend clean stains off her carpets recently using simply water and hydrogen peroxide alone. Just make sure you follow the instructions for the correct ratios of hydrogen peroxide to water.