Contrary to popular belief, not all encryption becomes completely useless. It just gets a whole lot harder. How big of a deal this is depends on the constant factors associated with the algorithmic reduction.
Reliable encryption depends on having a trapdoor function which is unfeasible to break in a "reasonable" amount of time. Choosing a trapdoor function whose compromise constitutes a problem in NP is an easy way to do that right now... but there's nothing inherent about problems that are not deterministically polynomial that makes them the only choice for things that take a long time. Pick a trapdoor function where, sure, it can be broken in n*log(n) time, but the constant factors make it take ten billion times longer than normal decryption anyway, and you've still got something useful.
Additionally, NP isn't the worst complexity class, by far. Which means that even if we can solve non-deterministic polynomial problems in deterministic polynomial time, cryptographers will just start looking for new non-polynomial trapdoor functions that can only be broken in, say, EXPTIME, or EXPSPACE. Since NP decryption is now potentially feasible, there's a much larger space of approaches to play with now.
So: present day encryption probably becomes insecure right away, and there will be an adjustment period while research continues into new approaches, but eventually we'll recover from that.
Aside from that, though, the world rapidly becomes a much better place, due to improved economic efficiencies. All sorts of optimization problems that were previously infeasible suddenly become trivial--at least, above a certain scale determined by the constant factors in the translated algorithms. That means pretty much every large business can save money, and consume fewer physical resources for the same results. Research in theoretical physics, chemistry, and biology also speeds up, as tons of things that were before infeasible to simulate become feasible to simulate exactly. That means less time and money spent on the first wave of lab experiments--we can weed out poor lines of research earlier, and find better lines of research easier, before moving on to confirming things in the real world. At the very lowest levels, we start getting more useful direct results out of lattice QCD simulations that help pin down some of the free parameters in the standard model; at the higher levels, we can have computers design specialized drugs by assembling atoms into bioactive compounds from first principles.