The good men shall do nothing and the bad men even less
It's a rather long distance to make prognostications across, but I'll venture a few broad ideas.
I think the international system will have signifigantly shifted. In two hundred years I could imagine that China and India could well have eclipsed the United States in power and by that distant point may be declining themselves and soon to be supplanted by rising South American and African powers (seriously, their luck can't completely suck for another two centuries... can it?). This alternation of powers could conceiveably also have some nasty wars or trade conflicts as a result, but not necessarily so. Trade tends to discourage major war and if globalization continues, the incentive not to disrupt trade may well preclude any military cataclysm.
The United States will probably still exist, but not in an immediately recognizeable form. Though it wounds my federalist heart to think so, I could imagine the United States having adopted a truly unitary system of government with every damned thing managed by Washington and state authority badly eroded. The other alternative is a more confederal system, quite possibly with regions (New England, Deep South, and etc.) having become the dominant element, but this is perhaps far fetched.
This all depends, of course, on the idea of the state enduring. It's a hoary old science fiction cliche, but the preposterous economic power possible with globalization could lead to corporations surpassing the majority, if not all, nations in wealth and influënce, making them far more important that what may be vestigial national governments.
Computer technology will probably have advanced so dramatically as to nearly escape comprehension. Things may slow down eventually, but there's still plenty of time left for the current rapid pace of advancement to continue.
Alternative and renewable fuels seem likely to replace oil by the two century mark. This is a matter of practicality, no matter how clever and creätive we are about squeezing every drop of the black beast from the Earth, by so far in the future I imagine that refinements and advancements in alternative technologies will have rendered oil comparatively uneconomical. Such could have unfortunate consequences for the middle east, which might see economic collapse and depression that drastically retarded social advancement.
I don't believe any horrifyingly drastic changes in social structure or morality will take place. Human sociëty is resilient and even if current religions and philosophies fall out of favor, sociëty will always subsconsciously recognize the need for some ubiquitous system of rules and courtesies as necessary to its continued existence.
Also, I predict that fedoras, bowlers, homburgs, and porkpies will come back in a big way. Sadly, so will bell bottoms and those stupid fabric extensions that make your pant legs look preposterously voluminous. I hate those damned things.
“What is earnest is not always true; on the contrary, error is often more earnest than truth.”