I have a strong affection for this particular Trek show (perhaps more than healthy), but it was a life preserver during a sustained life hardship.
What was so amazing about this series, was that it really seemed like it took place in some future time. The characters had a mentality that didn't fit the 20th century. They were written to be different from us. Some were put off, but many like me found it quite appealing.
In fact if you get a chance to watch "Encounter at Farpoint", there's a blink-and-you'll-miss-it scene in Q's courtroom where a machine gun-wielding bailiff is knocked to the ground by Tasha Yar and is summarily executed at the behest of Judge Q. There's a look of sadness on Tasha's face after it happens. That's a brilliant Roddenberrian touch.
Sure the series had its flubs and it had its forays into silliness, but the creative minds of the show learned from their errors and constantly worked to do something different. "The Ferengi were a lousy adversary? Let's try a race of cybernetic zombies." And very little went to waste! Q was shoehorned into the original pilot to pad into two hours, and inadvertently became one of the most fascinating and beloved characters in the Trek canon. Tasha Yar died in an unsatisfactory way in "Skin of Evil", but it became a unintentional set-up for one of the greatest episode of Trekdom, "Yesterday's Enterprise".
Gene Roddenberry dared to make Star Trek something bigger than Kirk and Spock. He gambled and won. But, he gave the show it's roots and a vision. Some of it was a little too funky for most of us. But, then stepped in the late, great Michael Piller who got the show working on all thrusters, and by and large helped create the foundation for 3 subsequent spin-offs (of varying quality).
I feel bad that the cast never got the proper send-off in the movies that the cast of the original show did in Star Trek VI:The Undiscovered Country. But, the series finale, "All Good Things…" was a brilliant coda, and one can easily write off the four feature films.
Anyway, if you're a fan of the show and you get a chance: watch a TNG episode in tribute to a show that paved the way for science fiction on television for the last quarter of a century.
[Me with the TNG cast at the 2012 Calgary EXPO. Yes I know, Patrick Stewart got the flash in his eyes.]
This is worth a read:
"How Star Trek The Next Generation Changed Pop Culture Forever" from Time Magazine.