Star Trek: Voyager a few times.
Q made only one appearance on Star Trek: Deep Space Nine. In the season 1 episode "Q-Less," the mischievous alien followed Vash - a former romantic partner of Picard - to the infamous space station. However, instead of the diplomatic patience of Picard or the pragmatic bemusement of Janeway, Q ran afoul of like Sisko as much as Picard.
Why Q Was So Fascinated By Picard And Janeway
Q had a fairly low opinion of humanity as a whole, but he did have a few favorites. One of those favorites was Kathryn Janeway; after seemingly bidding adieu to Picard in the TNG finale "All Good Things," Q's primary interaction with humanity was via the crew of the USS Voyager, the Federation starship that was trapped in the Delta Quadrant, decades away from Earth. Q thought so highly of Janeway he even attempted to mate with her, though that was largely to prevent a civil war among his people in the Q Continuum.
But there's no question Star Trek: Picard season 2, freeing Picard from a guilt he'd been carrying since his childhood and emphatically confirming what had been obvious for some time - Q genuinely loved Picard.
Q & Sisko Hating Each Other Ensured DS9 Didn’t Repeat TNG
The fact that DS9's early Q episode didn't quite work was a blessing in disguise. The show's writers took it as a sign that repeating TNG's triumphs was probably not a path to long-term success. The show would eventually blaze its own trail, embracing serialization and religious themes in ways Star Trek had never attempted, culminating in the epic Dominion War saga. There's no other Star Trek show quite like Deep Space Nine, and part of that legacy began with the show deciding what it didn't want to be. Q found plenty of places to enjoy himself in the Star Trek universe, but DS9 was not one of them.