The Roman Emperors kept the Senate because to have not done so would have invited levels of political opposition that could have proven destabilizing to the emperor's rule. The speculation provided in the above answer is accurate if one is to accept Edward Gibbon's description of the later phases of the Roman Senate's history:
"The necessity of finding some artificial support for a government which, from a principle, not of moderation, but of weakness, was reduced to negotiate with its own subjects, had insensibly revived the authority of the Roman senate..."[Gibbon, The Decline and Fall of the Roman Empire, Chapter 30; published between 1776-1789]
And, again, in the following passage:
"There appears, indeed, one memorable occasion, in which the Senate, after seventy years of patience, made an ineffectual attempt to re-assume its long-forgotten rights. When the throne was vacant by the murder of Caligula, the consuls convoked that assembly in the Capitol, condemned the memory of the Caesars, gave the watchword liberty to the few cohots who faintly adhered to their standard, and during eight-and-forty hours acted as the independent chiefs of a free commonwealth. But while they deliberated, the praetorian guards had resolved...The dream of liberty was at an end; and the senate awoke to all the horrors of inevitable servitude."
The history of the Roman Senate was one of considerable influence in the day-to-day affairs of Rome, especially in the earlier eras. While the emperors were omnipotent in the sense of being dictators, like dictators, they recognized that "spreading the wealth" and appearance of power was an important component of self-preservation. The emperors controlled the Roman Legions, but they were not invincible, and they accepted the Senate's procedures as a way of letting political allies and potential opponents have a forum for expressing their views in favor of or in opposition to the emporer's policies. In a more Machiavellian sense, Senate deliberations, in which opponents could be heard to express their discontent, was a good way of identifying the emperor's enemies.
The histories of Tacitus and Suetonius provide additional insights into the role of the Senate in Rome under the rule of the caesars. Tacitus had been a senator in Rome, and served as its historians. His Annals and Histories provide invaluable insights into that world, and worth the time spent perusing them.
We do not know for sure why the Roman emperors kept the Senate. They did not leave statements saying why they did so. Therefore, we have to speculate. There are at least two major reasons why they might have kept the Senate.
First of all, they might have kept it as a way to make it look as if they were not really becoming autocrats. We have to remember that before the era of the Roman Empire, Rome was very proud of its republic. Julius Caesar was assassinated in part because it was feared that he would destroy the republic and turn it into a monarchy. Therefore, keeping the Senate was a politically astute thing to do. It enabled the first emperors, in particular, to maintain the illusion of republican rule so that the people did not become upset with the move towards autocracy.
Second, they might have kept the Senate as a way to keep Roman elites happy. As the emperors were taking more power, there was less power available for the elites. However, if they could still be given senatorial rank, they could still feel important. The existence of the Senate, then, could act as a way to give prestige to people without giving them real power.