I visited a Glasgow crematorium as part of my work (don't ask!) and in the cremator room there were probably fifty jars of ashes, most of which had been there for a while without collection. They keep them a month then get in touch with the funeral director to see if the next-of-kin wants them. If not, they are scattered in the Garden of Remembrance. The containers which had been there for much longer belonged to deceased where there was no next of kin, and they were kept for a much longer period in case someone turned up to make a claim. The place was VERY dusty!
On a personal basis most people I know have used the Garden of Remembrance, either scattering ashes or burying urn, and some have scattered ashes over the graves of other loved ones.
My friend cremated her dog about 10 years ago and his urn full of ashes sits on her lounge unit; she does not however have any family members on display!!