To me, the major effect of the French Revolution was that it created the idea of nationalism in Europe. This idea came to be hugely influential -- it led, for example, to the creation of the countries of Italy and Germany. The creation of Germany, along with its policies that were based on nationalism, helped lead to WWI.
By helping to bring about these changes, the French Revolution affected the world in a way that continues to have an impact today.
In my mind, the most intense effect of the French Revolution was the ushering of despair and despondency behind grass roots movements and expressions of the political good. On the heels of the American Revolution, the conventional wisdom indicated that populist- led movements can inspire lasting change and radically transform disproportionate uses and displays of power. The Romantic thinkers at the time believed in the "bliss" of the French Revolution because of this. However, the Reign of Terror and the presence of mob rule reflected how populist expressions of the good can move very quickly to realms of anarchic displays where the public good and safety are ultimately undermined. The fact that the French Revolution started out with such pure intentions of change, but then quickly devolved into the consolidation of power by an elite few who ended up relying on the passions of the many to fulfill their own agenda became one of the lasting effects of the Revolution. The Reign of Terror represented one of the most brutal representations of government. Within this element, and the eventual seizure of power by Napoleon in the desires to maintain public order, one of the lasting effects of the French Revolution was to show that declaring independence and preserving it were two vastly different elements.