If the microwave is still in good condition but needs a few repairs to make it run well again, consider taking it to an appliance repair location. A repair often times costs less than replacing the microwave completely.
Thrift stores and charities take broken and unwanted older appliances such as microwaves off of people's hands, generally at no cost to you. This way, your microwave gets refurbished to help a less fortunate family and can, in some cases, count as a tax-deductible donation.
Microwaves consist of a number of valuable recyclable materials, such as steel and aluminum. Your microwave can be taken to a recycling center so that it may be broken down and recycled. Depending upon your location, appliance recycling services either pick up the appliance or have a drop-off location. This can be found on your city's government website or by searching the phone book for recycling services.