When I grew up (in the 50's early 60's) the big deal was to get ones white laundry whiter than white.  To do this, mom added bluing to the water.  That, plus hanging the wash on the line to dry in the sun, got a brilliant white result.  What I do today, is wash my blue shirts with my white undies and sheets. The blue shirts are the modern day bluing.  Actually, because of the private nature of my laundry, only I know it's whiter than white.  But it is.

Doesn't the blue bleed into the whites?  How does this work?  I'd love to be able to get my whites whiter without bleach.

You can still buy bluing.  It's called Mrs. Stewart's and comes in a blue plastic bottle.  I've found it in several grocery stores, usually tucked somewhere on the top or bottom shelf of the laundry detergent section.  You dilute a few drops (a bottle will last forever!) and add it to the rinse c ycle.  If you use too much, it will tint the clothes blue, but in the right amount, it just makes whites sparkle!