James,
Like most people we use all of the usual suspects, sodium met, shift, spray & go etc etc, but with the best will in the world the really though stains are at best hit and miss, most often because they have been tampered with. The thing is never to guarantee, or even suggest that you can get the stains out, only that you have all the latest stain removal products and you will do your best. The problem is that stains can sometimes be the reason they called you in the first place and unless you qualify the customer adequately and revise their expectations downward, to you'll do your best, but can't guarantee complete removal then you may have a dissatisfied customer on your hands. The same applies to very dirty or heavily worn carpets as you must always be aware then when they are on the phone to you, in their minds eye is a carpet that looks like it did when it was new and our job is to adjust that mental image and modify their expectations through qualification so that what you eventually produce is more in keeping with that new expectation and possibly well beyond it if all goes well.
Simon