If it is just old, I cherish it. I don't have any that are actually dirty, anytime anything ever gets on any of them I wipe it off immediately to avoid stains, and if it is a fabric bag as soon as I get home I will spot clean it with an old toothbrush and whatever harmful chemicals I think might help.
The exceptions would be my blue denim bag and my old green canvas Chinese Youth Corp or whatever it is called, (like the one Cameron Diaz got so much publicity from, except I got mine for 50 cents at a thrift store about twenty years ago) and those I just throw in the washing machine and dry them in the dryer.
If yours is a bag you like except for its dirty former whiteness, why not help it become a different color through the magic of a Makeover!
If it is leather, you can use shoe dye, if it is unleather, you might be able to use shoe dye, but on unleather you can use almost anything, you could use acrylic paint and polyurethane it, make it a solid color and stop there, or decorate it with stencil designs, or just draw them if you can draw - unleather lets your imagination soar!
Edit to note for the benefit of the historical docentical crowd, I actually have two of those old Chinese bags, and one does enjoy a life of leisure and is just displayed, but the working one looks as "new" today as it did when I bought it, considering that it was already "vintage", and putting it in the washer and dryer has not hurt it one bit.