See post 6.
I come up with:
Three Italian wars of independence against Austria, in the last case allied with France.
Two Danish-German wars over Schleswig. (Not the best idea the Danes ever had!)
The Crimean War: Britain, France and Sardinia vs. Russia.
The Austro-Prussian War.
The Franco-Prussian War.
The Prussians were thus involved in four of the eight wars.
I haven't really compared this to other centuries in detail, but I seriously doubt there is another 100 year period in European history with fewer wars.
Yeah, that sounds about right. It depends if you want to classify attempted revolts and revolutions as "wars". I think the Hungarians tried one against the Austrians that the Russians helped put down. The 18th century was much more violent than the 19th, at least as Europe proper is concerned.