Having your dog cremated allows you to hold onto a small part of him after he passes on. What you get back from the vet or crematorium depends on the service you request. Typically, unless you request a private cremation, he will be cremated at the same time as other pets, and there may be an unavoidable comingling of ashes -- this means you may be getting back a portion of someone else's pet mixed with yours.
Private Vs. Shared
When your vet offers cremation services, ask what type of cremation are available. This service is typically outsourced to another agency that returns the ashes to the vet. If you request a private cremation, you will pay more, but you have some assurance -- let the buyer beware -- that your dog is being cremated by himself and the ashes returned to you are his alone. Otherwise, his body will be cremated alongside other pets, with or without a partition between them. Services vary. Without a partition, the ashes of the cremated animals will mix together; even with a partition between dogs, when the ashes are collected they may mix a little. In any case, don't expect a large volume of ash -- your dog's body is largely composed of water; even the average human generates only about 5 pounds of ash after cremation.