Call your electric company to ask about bounty programs. These programs pay you for disposing of your old refrigerator, and pick it up for you. Not all styles of refrigerator are accepted, so know the make, model number and size of your mini fridge before you call. If this program is available to you -- not every community has this -- make an appointment.
Contact your town's Department of Public Works for information on refrigerated-appliance disposal. Communities may ask you to bring the item to a landfill or leave it curbside; they may request you schedule a pickup and pay a fee.
Ask the appliance manufacturer about old model pickup, if you're replacing that mini fridge with a new miniature or full-sized refrigerator. This might entitle you to free pickup of old appliances. If you qualify for free pickup, unplug and clean out your mini fridge before you get the new appliance delivered, then make sure the deliveryman takes the old fridge.
Donate mini fridges that still work to charities that could use them. Try senior centers, youth groups or animal-rescue organizations, who may need refrigerator space.