For twill and jacquard (signature) bags, try using diluted Woolite. I've done that before for spot treatment and it works well. Clean the area with warm water afterwards to prevent staining.

DO NOT use Oxyclean or Shout Wipes or anything like that on your bags -- those make your bags end up looking worse! They tend to leave nasty residue stains and can cause discoloration.

For leather/suede, I'd take it to a speciality cleaner, use Coach leather cleaner, or bring it to a store.