Hume's proclamations were so drastic that he disturbed the "dogmatic slumbers" of a frail, gentle man who also later became recognized as having one of the greatest minds of all time. Immanuel Kant's newfound inspiration led to his completion of his Critique of Pure Reason which, among other things, bridged the gap between rationalism and empiricism. Kant believed that knowledge begins with experience, but that the experience awakens our innate mental faculties. Our senses and our mind are both active agents in creating knowledge: "Thoughts without contents are empty; intuitions without concepts are blind.”
I adhere, as I assume most post-Kant thinkers do, to Kant's merging of the two views. I know it is possible for my senses to be tricked, by optical illusions or what have you, but I still believe that can be accounted for and that we should trust them, we just shouldn't deem them to be the sole basis of all knowledge. With no raw data, I do not think we should participate in speculative metaphysics--we cannot rationally prove something like the existence of God without empirical evidence--a belief in God requires a leap of faith and has no business involving itself with science or logic (not to say that science and logic don't require a leap of faith themselves.) Today there is a general respect for science that would make an empirical view easier to hold with confidence; but the mind is far too mysterious and its power too riveting. When I look at a painting, I'm looking at millions of tiny droplets of color, yet my mind is able to decipher these into discernible figures and shapes. Mathematics is a good way of showing how both rationalism and empiricism are both important components of knowledge. Some rationalists believe that we are able to understand something like the number three as being prime and greater than two a priori. This is something I disagree with; numbers are not things in themselves. I believe they are man-made constructs that we use to more conveniently operate and organize our empirical perceptions. Once we are able to fathom this established concept of numbers, however, our minds are then able to rationally create and understand numerical patterns--using these abstractions which we know to already be accepted as true, we are able to use deduction the way Descartes proposed to create new, unique truths. It is in this manner that Sir Isaac Newton had the ability to sit down and invent calculus: he didn't find it buried under a rock; he created calculus by combining his previous knowledge with his innate mental faculties.
It is too far fetched to believe the mind is an inactive participant in the production of knowledge, and to be honest, I probably would have had to live in the 17th century to understand why this conclusion took so long to manifest itself through Kant. In football, say, when a quarterback throws a touchdown to his wide receiver, there is no debate as to which player was the active participant it is simply accepted that both players are responsible for the successful maneuver. While my example may be a bit lousy, if you ask me, the rationalist/empiricist dichotomy is no dichotomy at all the senses and the mind are both undoubtedly necessary.