Australian Cattle/Heeler dogs frequently have their tail docked. They tend to have a very floppy tail if they don't, in my experience. If properly done, it happens within about three days of birth... when I volunteered at a clinic for a while in high school, I was horrified to find out that it's done without anesthetic, until I watched a trio of purebred German Rottie pups get docked. They literally slept through it. Didn't even twitch when the tail got cut off. A couple days later they were back for an exam, and looked completely healed up. It's usually done to breeds that have problem tails - Rotties, apparently, are prone to breaking their tailbones whacking them into things if not docked - or herding and hunting breeds that are prone to bringing home half the woods, and all the briers in their tail if they aren't docked.
It's not done on all, and doesn't need to be done on all. My Aussie mix has a full, very waggy tail, but she's also not out herding cattle in the brush.
Now, ear cropping... I still have no use for that. It's painful, prone to infection, and I've yet to find a viable reason for it unless the dog's had an injury to the ear requiring it to be cut off. Purely aesthetics, and I tend to think dogs look better with ears. Ever seen a natural Doberman, with floppy ears and a long tail? They're gorgeous!