Used razor blades are still dangerously sharp and can cause serious injury if thrown away without precautions. Stainless steel and carbon steel blades can be recycled, but most importantly must be isolated from the possibility of harming others.
Blades can be wrapped in the paper they were shipped in, or in several layers of paper; but this method is far from foolproof and is not particularly convenient. Blades can be inserted into the bottom portion of some plastic blade dispensers; but again, this method is not particularly secure unless the plastic dispenser is taped shut.
Used razor blades may be considered medical waste; it may be useful to consider them as such when examining the possibilities for disposing of used blades. Check with your local government regarding laws and ordinances regulating disposal/recycling of used razor blades.
Gillette and GEM provided blade storage boxes that were attractive and durable enough to serve multiple purposes: Gillette's were re-purposable as used blade storage or match boxes, and the Bakelite boxes of, e.g., the GEM Micromatic had separate storage for new and used blades (see here for a picture). Similarly, the 1912 GEM Deluxe was sold with a blade bank in the case.
Non-commercial blade banks
Several inventive shavers have found multiple ways to store "sharps" (blades) without a commercially produced blade bank. Two popular methods are storing them is large pill bottles, or constructing a blade bank by cutting a slot in the top of an empty soup, broth, coffee, or condensed-milk can.
Older construction houses and hotels
Collectible Blade Banks
 gave blade banks away as promotional items (giving them free advertising space in the bathroom, where the users would see the blade bank every morning). Some blade banks are shaped like objects associated with barbering (barber poles, e.g.), while others exist resembling animals and cars, in addition to the decorative metal boxes.