A square bottom plastic bag is designed to stand upright when opened. The bags are constructed with open tops, side handle openings and attached headers or with t-shirt style handles. The bags are produced in registered bag stacks and include means for adhering a rear surface of one bag to a front surface of a subsequent bag to make the bags self-opening when used with a dispensing rack. The headered bags have tear-off headers or headers with weakened areas that will rupture upon dispensing. The t-shirt bags have apertures through the handles to suspend the bags on a rack or a header attached above the handles. The bags have detachable or rupturable center tabs. The bags are registered with hot pins or cold stakes through an upper portion of the bags or bag handles. The bags have openings, microperforations, or are formed of porous material to dissipate heat or moisture.