Now that Mubarak is out, it will probably take awhile to determine the ultimate outcome from the perspective of U.S. policy and our relationship with Egypt. At the moment the military is in charge. It has extensive ties with the U.S. As long as the generals hold the reigns, barring some sort of unforeseen radical shift, there shouldn't be any major changes in our relationship with Egypt.
Will the Egyptian military make good on its promises, release its hold on power and allow truly free elections? Maybe. But it's also possible that it will retain significant control over the country, allowing only a facade of democratic rule -- more than Mubarak, but less than most desire. If true democracy does take hold, all bets are off. I don't believe there is much the U.S. can or should do to influence the process in Egypt. It is far from clear that a democratic Egypt is in the U.S. interest, given many of the attitudes present among the population, and that fact that we are already strongly associated with the decades of authoritarian rule.
I understand the celebrations in Egypt. If I had to live under the Mubarak regime I'd be happy it was gone also. But that doesn't mean his fall is a good thing for the U.S. Maybe the wishful thinking of Obama and even many on the right will be proven correct, and a friendly, free and democratic Egypt will take the place of Mubarak. I'll believe it when I see it. Right now all we can really do is wait and see, and hope for the best.