I wouldn't. Once we get our 'pets' - we fall in love (or in some cases - don't) but in my opinion - why would I care ? They are what they are and no test would make me love them more or less.
Health wise - don't know - I don't think a DNA test would really offer much information on what is in the lines.....The only thing I can think of where they'd be handy is if a breeder was questioned on who a mom / dad was regarding a puppy. But - hopefully MOST OF US ARE NOT BREEDERS
(there's already way too many people breeding) then that really doesn't apply to a average person.
ps - edited to add - doing it for fun is totally different. Can't see any thing wrong with that !