Drying racks are racks for drying. Not too complicated. You put your beakers, cylinders, vials, etc., on one of these bad boys and watch gravity do its thing.
The big advantage of these models is that they're more durable and portable than the rack in your dishwasher. Available in multiple sizes, configurations (wall-mounted or self-standing) and materials (like high impact polystyrene and epoxy-coated steel), professional-grade drying racks are found in almost every lab.
Unfortunately, as with a dishwasher, you still have to unload the thing.