TL;DR: Not really. After all, most lesser species are so... dull.
The entity known as Q is known - especially in the Q Continuum - as a troublemaker who enjoys messing with lesser species, often tormenting them in the name of "fun".
Out-of-universe, the reasons are obvious - we are only seeing the crews which are a focus of the shows, so naturally it's THEIR experiences with Q that we are witness to. However, there are valid in-universe reasons why these encounters happen.
That said, he initially encountered the NCC-1701-D as they were - at that time - the furthest Federation vessel know to the Q, and were therefore chosen as an example of the Federation's exploratory & adventurous nature. This initial encounter impressed Q, and he quickly became somewhat infatuated with the crew, especially Captain Picard, whom he came to view as something akin to a beloved pet.
"... in all the universe, you're the closest thing I have to a friend,
Jean-Luc." -- Q; TNG S03E13
Q's visit to DS9 was not due to any interest in the station or crew, but instead on the woman Vash, who had returned to the Alpha Quadrant via the Bajoran Wormhole and therefore found herself on DS9. Q attempted to play with Benjamin Sisko as he had Picard, but quickly learned that Sisko was simply "no fun" to play with.
The USS Voyager only got the attention of the Q Continuum after accidentally releasing an exiled member of the Continuum from the comet into which he had been imprisoned. He quickly found a new, unsuspecting plaything in Captain Janeway, however, whose stern manner reminded him very much of Picard.
Beyond the encounters with Picard & the other crews, Q had very little interest in either Earth OR humanity. He and the Continuum in general certainly had very little interest in the current cultures on Earth, instead seeing humanity only for its potential in the eons to come.
"An abysmal place, Earth. Oh, don't get me wrong. A thousand years ago
it had character: the Crusades, the Spanish Inquisition, Watergate.
Now it's just mind-numbingly dull." Q; DS9 1x07
We know from various episodes that Q had tormented other races, not only once but several times - certainly enough to garner a negative reputation throughout the galaxy.
When he became powerless and sought refuge on the Enterprise-D, it became obvious that numerous races hated Q enough to hunt him down while he was vulnerable. The Calamarain were the first to arrive, but Q seemed fairly certain that others would be coming as well.
For instance, Q had tormented the inhabitants of Brax enough that he was known in their culture as the "God of Lies". This would seem to indicate a definite pattern of behavior, rather than one or two encounters on the planet.