The American Revolution was undoubtedly a success in its immediate aims of ending British rule and establishing a system of republican self-government. It was less successful, however, in putting republican principles into practice. The biggest stumbling block was slavery.

As British critics of the American colonists never tired of pointing out, demands for liberty sounded pretty strange coming from slave-owners. To be sure, many among the American political elite understood that slavery was something of an anomaly in a nation supposedly founded on liberty and equality; indeed, many slave-owning politicians felt the same way. But for one reason or another they were unable to square the circle.

The states had just thrown off the shackles of British rule and formed themselves into a loose confederation. The last thing anyone wanted was for the new arrangement to be jeopardized by squabbles over slavery. If concerted action had been taken to end slavery then it's almost certain that the Southern states would've seceded, thus plunging the new nation into the mother of all constitutional crises. As no one really wanted that, the problem of slavery was left for later generations to deal with, with tragic consequences. This inability to deal with the fraught issue of slavery is one legacy of the American Revolution that was emphatically not a success.

I suppose to a certain extent, the answer to this question depends on which country you are from (or which country you most sympathize with). To an American, yes, the American Revolutionary War successfully gained the American colonies independence from Great Britain. To a British citizen, that same war ended in an embarrassing defeat. Great Britain had a more well-trained army and a much better equipped navy. On paper, the British had just about every advantage conceivable, yet they lost. The goal of the American Revolution was to gain independence from the British. This happened; therefore, it was a success. It may have perhaps taken a bit longer than the original goal, or it resulted in far more casualties than initially predicted; however, that does not change the fact that the end goal was achieved.

It would be very difficult to argue that Revolution was a failure.  You could argue that it did not accomplish everything that it should have, but you would be hard-pressed to say that it was not an overall success.

You can argue that the Revolution should have led to a truly democratic society in the US, one in which women and African Americans were treated as the equals of white men.  Ideally, this is true.  But there was no way that was going to happen at the time and equality for all was not one of the goals of the rebels.  

The Revolution was a success because it achieved what it was trying to achieve.  It was meant to gain independence for the United States and it accomplished this goal.  When some movement accomplishes what it sets out to achieve, it is a success.