Knowing the answer to Poincare's conjecture won't build you a better toaster oven tommorow. There's no way that not knowing the answer to a "yes/no" question (which is what Poincare is, really; "Is everything that with the same algebraic data as a sphere necessarily a sphere?" "Yes," as it turns out.) can really impede technology. If some technology really depended on knowing the answer to Poincare you'd just go ahead and build it, assuming it was true, and if your gadget failed unexpectedly, well, then you'd have learned something.
So the primary benefit of Perelman's work is not the answer to the a big question, but the techniques he developed in the process of tackling it. The machinery of Ricci flows almost certainly will benefit applied mathematicians in a lot of unanticipated ways, and mathematicians and engineers who could not possibly have refined the machinery the way Perelman did can still use it now that he has.
That's the practical benefit of big, "pure" problems like Poincare and most of the Clay Institute problems. The answer to the question itself isn't as important as the machinery that has to be built to get there. Once an engine is built, industrious people will always find a way to drive it interesting places, even if the guy who invented it regarded it as an end in its own right and doesn't care where it goes.
By way of comparison, look at how much effect the answer to Fermat's Last Theorem has had on the world (I would say essentially none), versus how much effect the machinery of elliptic curves, which was refined enormously because of pure mathematicians' interest in the Fermat problem, has had.