I'd be surprised if that were true but maybe. Most of the episodes I recall seem like they were encountering something strange and interesting while in space, encountering new and different cultures.
Despite it being the party line, there really isn't much exploration in Star Trek. To examine the point in TNG, let's take a look at the first five episodes of each season:
Encounter at Farpoint: Basically heading off to the Farpoint outpost to pick up their crew gets sidetracked at first by Q and later they have to sort out why the alien jellyfish is so interested in Farpoint.
The Naked Now: Responding to a distress call. Crew then gets infected.
Code of Honor: They go to the planet to get a vaccine needed on another planet.
The Last Outpost: The episode starts with them dealing with the Ferengi attacking and stealing from a Federation outpost. Only because they happen by a planet which interferes with both ships do they go to the planet to check things out and learn about the civilization that lived there.
Where No One Has Gone Before: The Enterprise is undergoing engine experiments when they are thrown to a distant part of the universe. I suppose there is exploration in this one, but it's accidental.
The Child: Between acquiring their new CMO and transporting biohazard material, an alien entity boards the ship and impregnates Deanna.
Where Silence Has Lease: The Enterprise is dragged into another region of space by an alien douche.
Elementary Dear Data: The Enterprise is literally sitting still waiting to meet up with another ship, so Data and Geordi go to the holodeck and accidentally create a sentient hologram.
The Outrageous Okona: While just passing by, the Enterprise responds to a request for help.
Loud as a Whisper: The Enterprise transports a diplomat to a war-torn planet.
Evolution: The Enterprise hosts a visiting scientist.
The Ensigns of Command: While the Enterprise deals with an approaching alien ship, Data visits a colony to convince the people to leave before said alien ship arrives.
The Survivors: The Enterprise responds to a distress call from a colony.
Who Watches the Watchers: The Enterprise responds to a distress call from another group of explorers. I guess there is exploration being done in this one, just not by the Enterprise.
The Bonding: This one actually does start off with the Enterprise doing some exploring, though ultimately the episode isn't really about that.
The Best of Both Worlds, Part 2: Pretty much defending the Federation and rescuing Picard.
Family: The Enterprise is parked in Earth orbit. Picard visits his brother and family, Worf's parents visit.
Brothers: The Enterprise is rushing to a starbase to meet the medical needs of a child on the ship when Data is hijacked and himself hijacks the Enterprise.
Suddenly Human: The Enterprise responds to a distress call.
Remember Me: After the Enterprise leaves a starbase, Dr. Crusher gets stuck in some sort of pocket universe.
Redemption Part 2: Picard puts together an armada to try to prove Romulan involvement with the Klingon Civil War.
Darmok: Aliens reach out to the Federation to open diplomatic talks. Tangentially related to exploration.
Ensign Ro: An Evil Admiral manipulates the Enterprise dealing with Bajoran terrorists.
Silicon Avatar: The Enterprise as transporting colonists to a planet to settle on, planet gets attacked by the Crystalline Entity, the Enterprise spends the rest of the episode dealing with that.
Disaster: The Enterprise is disabled.
Time's Arrow Part 2: An Earth-bound adventure, for the most part.
Realm of Fear: The Enterprise responds to a distress call.
Man of the People: The Enterprise is transporting a diplomat to a conference.
Relics: Okay, this one does have exploration.
Schisms: Aliens abduct the crew.
Descent Part 2: Dealing with Lore and his band of independent Borg.
Liaisons: The Enterprise hosts alien diplomats while Picard is stranded on an abandoned planet. I guess you could say there is exploration, but it's the aliens doing the exploration here.
Interface: While experimenting with new technology, the Enterprise responds to a distress call.
Gambit: Investigations into Picard's apparent death lead the Enterprise into a fight with space pirates.
Phantasms: The Enterprise leaves a starbase after getting a new engine, which breaks down, turns out to be a threat to the crew, and to save the day, the crew must interpret Data's nightmares.
So out of those thirty-five episodes, about seven are related to exploration and most of the time only incidentally so, which actually works out to 20% exactly, as
Vger23 asserted above.
