Some dogs are born with no tails - there are quite a few breeds where that is common.
Some breeds, because of the original use of the breed, are traditionally docked.
Some dogs have had tail injuries and had them docked.
While I would never set out to have it done to a dog I was getting (not that you can normally choose - it's done at only a few days old I believe), I do own a docked dog, who I got as an adult. It doesn't seem to affect her in any way, and it is just as expressive and read-able as any full tail I've seen.