There weren't really any major land battles on continental European soil. The conflicts surrounding the American War of Independence were mostly fought in European colonial territory, particularly in the [Caribbean](http://en.wikipedia.org/wiki/Capture_of_the_Bahamas_(1783)) and in India. Some historians, like Jeremy Adelman, view the entire period during the so-called "Age of Revolutions" as essentially a series of imperial conflicts.

There were, however, plenty of naval conflicts around the globe, including some near Europe. When the Netherlands went to war with Great Britain, there were plenty of small naval battles in European waters.

Part of the reason behind Spain, France, and the Dutch joining against Britain was to expand their power base and influence over greater areas. With Britain tied up in a major conflict in the Americas, it diverted British forces from other theatres and (ideally) made them weak enough to be vulnerable. Unfortunately this wasn't as true as they had hoped.

The largest battle of the American Revolution was the Siege of Gibraltar, in which Spain and France attempted to take Gibraltar from the British. In the end the British managed to survive a 3 year 7 month long siege which is to this day the longest endured by the British military. And the were horrible outnumbered and outgunned. http://en.m.wikipedia.org/wiki/Great_Siege_of_Gibraltar

Also, the last battle of the War was a naval battle in the Bay of Bengal, India.

Most of the other conflicts were smaller in nature, but yes, they did occur.