Within each breed you can usually do some sort of sport... Correct me if I am wrong... (And remember, I'm counting showing as a sport/hobby).
Well, me and my dogs partake in trail scenting where the dogs chase a scent and you follow on horseback - those that turn up at the right destination in a certain amount of time are awarded points, etc.
Agility is also a good one that alot of breeds can take part in but for my breed (bloodhounds) it's not recommended.
But, with my older boy (this is going to sound stupid) I have spent years teaching him to catch a flying disk (i would put the common name which sounds like risbee but it's commercial and could be seen as advertising :D).
Anyway, you see these disk competitions in America on films and documentaries but do they ever exist over here as I haven't seen them but I may not be looking hard enough!
I would love to enter Rover in one of these competitions. Very much doubt we'd win but it seems like such a fun, informal competition to enter. It would be properly playing for the fun of it (as some people say agility is).
Anyway, it's just a thought!