It would be wrong of us to say that no over the counter or DIY spot removal methods work, of course some do. However, we often see situations where over the counter and DIY spot removal attempts damage the carpet or rug far worse than the original incident. With the right information you can be well equipped to deal with a broad range of situations. See our blog post How to be Prepared for Spills on Carpet for more information.
Over the counter products are formulated to remove stains, but often with a "by any means necessary" directive. This means they load their products to the brim with detergents, surfactants, oxidizers, etc. By creating their products with such powerful chemistry they increase the odds of spot removal, but they also increase potential for damaging fabrics and leave heavy residues behind. Even with professional equipment there are some over the counter products that we can't practically rinse from a carpet. In a major industry distributor's spot and stain removal guide there is a how to section for removing a popular over the counter product from carpet, the suggestion is dyeing or a structural repair.
DIY spot removal guides on the internet want you to play chemist in your home, its simply not worth it. Never mix any two products together. While it is unlikely, you never know when two things may interact unfavorably or dangerously. There are a few household products that can be helpful in cleaning your own carpets and rugs, they should be used alone and never mixed: isopropyl alcohol, hydrogen peroxide, laundry detergent, baking soda, and vinegar. Look for blog posts with specific examples of when you would use these products.