During the Principate water carried by aqueduct was channeled into castella, which literally means "fortresses" but when talking about aqueducts refers to these reservoir-like structures that channeled the main pipe into smaller distribution pipes. Initially all water entering these reservoirs was for public use and it was forbidden for private citizens to use their own pipelines to divert water for private use. By the time of the Principate this had changed and private citizen were allowed to insert their own pipelines into the reservoir system and channel off water to their own homes. By Frontinus' day (around 100, A.D.) private citizens were constructing their own private reservoirs to prevent the intentional damaging of pipes and collection of the leaks that would result.
The (legal) private use of water was, however, always a monopoly of the wealthy. The right to divert water for private uses was, in the Principate, a complicated series of licenses and fees. According to Frontinus by the ruling of a senatus consultum under Augustus it was forbidden to insert private pipes except without the emperor's permission and without a license and it was forbidden to exceed the amount (measured by the width of the pipe) allowed in the license. Upon the grant of a license it was the duty of the curator aquarum (more on him in a bit) to oversee the construction of the diverting pipeline--Frontinus says that beginning with Claudius this overseeing was done by an imperial freedman on behalf of the curator. There was also some sort of fee involved, and rights to private water leading to a particular piece of property had to be renewed with each new owner of that land, including heirs who inherited through wills.
Despite these regulations, fraudulent tapping of the public water supply was extremely common, and a problem that Frontinus (who was himself curator aquarum) complains about a lot. Following Augustus' senatus consultum it was forbidden to collect water that was coming from leaky or damaged pipes, but it was still done anyway. In particular Frontinus says that people would often puncture the pipes outside of the city and divert them to their villas and fields illegally. He also complains of people fraudulently stamping their private pipes with widths that were not in fact correct, or illegally failing to stamp them at all. This fraud, as well as the (pretty funny, if you ask me) practice that Frontinus accuses some heirs of doing, namely renewing their rights for private water and building a second pipeline to their property instead of using the old one, so that they could sell the excess from the original pipe, points to the serious problem of bribery that existed with the regulation of the water supply. Officials in charge of inspection and maintenance of private and public water pipelines were constantly being bribed. While very serious punishments existed for fraudulent misuse of public water supplies (in 9, B.C. the consul Sulpicianus passed a law instituting a fine of 100,000 sesterces for the illegal tapping of public water pipes) but oversight was imperfect. During the Republic inspection of water pipes wasn't really part of the duties of any magistracy, and often the aediles simply filled in since in theory it fell under the general umbrella of their duties. Augustus set up the curatores aquarum, three special commissioners whose duties were to maintain and inspect the water supply. Naturally these curatores had enormous staffs--under Augustus the curators were staffed by 240 slaves paid for by Agrippa, and Claudius increased it to some 460. Besides this there were various freedmen and subordinates to the curators, whose duties beyond minor repair were the constant inspection of the pipes. In addition to bribery of these officials, bribery of the private contractors who conducted major building projects or serious repairs must have also been extremely common, which Frontinus hints at.
For the details of the legal aspects of the water supply, which are probably too complicated and intricate to lay out in full here, Frontinus is our major source, and you should probably consult him if you're really interested in this sort of thing. Frontinus was a curator aquarum and apparently took his office very seriously. In particular his discussion of water fraud and other legal matters is petty stupidly (and boringly) detailed