Different quenching agents are used in different reaction assays, targeting different components (which may not be found in all reactions).
Acids are able to denature proteins, ceasing enzymatic function, by protonating molecules. This prevents a reaction from progressing, and can be useful where the concentration of reactant and product is being studied.
Chelators, such as EDTA, can be used to sequester metal ions. Metal ions are essential in the catalytic function of certain enzymes, helping arrange the substrate correctly for the catalytic process. Removing these ions suppresses / ceases the catalytic activity of these enzymes (which include polymerases and endonucleases). As not all enzymes contain metal ions, chelators are unlikely to work with non-metalloenzymes.
Inhibitors can also be used with enzyme-catalysed reactions. Suicide inhibitors, which never release their target enzyme once bound, as well as very high concentrations of competitive inhibitor (which could cause issues with the assay technique used afterwards, by overwhelming the detectors with the concentration of competitive inhibitor) are both suitable. Some enzymes may not have specific inhibitors, or there may be off-target effects (unlikely in vitro), which could make using these molecules challenging. There is potential for monoclonal antibodies (Mabs) to be used as inhibitors, however these can be expensive and challenging to obtain. Mabs would be highly specific and can be designed for virtually any target.
Precipitants are used to take a reactant or product out of solution. This can allow concentrations to be determined at specific time intervals, allowing a reaction to be studied by quenching.