All of you have valid, thoughtful answers. The reason I asked this question is because I'm not entirely sure what my own answer would be.
Rationally, my answer is "no." I know that there is an overpopulation of dogs and cats; too many pets are in need of homes to justify creating copies of a departed pet. And I know that clones aren't identical and each have different personalities; although physically the same, a cloned pet may behave completely differently. Furthermore, I also know that the current science is imperfect -- "not quite right" clones are frequently produced and subsequently put down. I could never accept having a hand in producing animals only for them to be euthanized, but if that were not the case... Well, then, emotionally, my answer would probably be "yes." I had my beloved pet cat, Elvis, neutered when he was 5 months old. When he passed away at the age of 18 a little over a year ago, I would have loved for him to have had offspring. They wouldn't have necessarily been like him, but some part of him at least would have lived on. In that sense, the idea of cloning, to preserve some small piece of the departed, is enticing.