The French Revolution of 1789 initiated revolutions in a number of European countries, replacing the idea of a monarchy with the idea of a republic built on enlightment ideals. Which European countries escaped the turmoil and why?
Most of the government changes in the wake of the French Revolution were at the point of Napoleon's (very effective) sword, and were ultimately undone by the sword as well.
Where you get dramatic internal-driven change wasn't really after the first French Revolution, but the Second (1848). This touched off a series of Liberal revolutions which today we might call a "European Spring", although over 50 countries all over the world were affected.
England itself escaped, probably because it already had a relatively Liberal government. Ditto for the Netherlands. Russia, I'm guessing was not quite ready. Their definitive revolution had to wait for 50 years. The Iberian peninsula also escaped relatively unscathed, chiefly because they'd just finished similar wars a couple of decades earlier.
One of the lessons a lot of leaders (Bismarck prominently excepted) took from 1848 was that having a relatively liberal government, like England and the Netherlands, Spain, and Portugal, actually appeared to make your country more stable in such times. This caused a lot of "Liberal" reform to be voluntarily instituted over the next few decades.
Polish-Lithuanian Commonwealth didn't have any revolution that was inspired by French one. Because of the strong belief in the ideas of enlightment among the court and nobility, in 1789 the country was already in the time of drafting their own constitution, what in 1791 was finalized with signing the Constitution of May 3.
That led to Polish–Russian War of 1792 that is also called War in Defence of the Constitution. The lose of it soon led to Second Partition of Poland, as Frederick William II of Prussia demanded Greater Poland as a recompense for cooperation in the coalition against French.
The reaction fow that was Kościuszko's Uprising in 1794, which was quickly followed by Third Partition and the end of Commonwealth of Poland (which was a new constitutional name of previous Polish-Lithuanian Commonwealth).