In Dublin and Belfast, it seems to be fine to let your dog off the leash. As long as it doesn't bother anybody. It's kinda bad form to let your dog just ... wander, but I don't think it's illegal.
The only caveat is that if your dog worries sheep (i.e. out in the countryside), a farmer might shoot it. So don't let your dog worry sheep. It'll get shot. (Folk don't let their dogs run wild in the country, just in the city and suburbs.)