This site focuses exclusively on the original 79 episodes (the so-called "seventy-nine jewels") which were made in the late 60s. To me, these are Star Trek like nothing else. Everything since has been, well, something else.
That's not to say that the movies were not good. I quite liked The Wrath of Khan and The Undiscovered Country. But they never captured the feel of the original series. Each has a sense of class reunion about it, coupled with twisting and turning to get each cast member at least one big scene, and generally tortured and failed attempts to evoke the spirit of the original.
They also tend to feature derivative stories, lame humor, excessive emphasis on special effects, unsatisfactory endings, questionable characterizations, hokey dialogue, etc. Some of the movies are downright bad, and would actually rank below the lowest quality episodes of the original series. Fortunately, nothing in these films (unlike later series) actually taints the original (except, perhaps, The Final Frontier). Likewise, nothing illuminates it.
My solution is simply to consider them as something else entirely and view them in that context. The show and the movies are two different animals and should not be compared.
Because the original episodes keep giving and giving (profit-wise, that is), they became known within the studio as the "seventy-nine jewels."
In 1987, DeForest Kelley used the name at a convention in response to a question about residuals (money paid to actors each time the show is rerun):
"How do we feel about not being able to participate in the royalties of the videocassettes of the motion pictures? We want to cry, don't you know. A lot of people are under the impression that we get residuals from the series. We don't, you know. We did for three years. And at that time the Screen Actors Guild had a contract that after the first year we got paid for seven reruns, the second year, eight reruns, the third, ten, and that's all, and that was all that we were paid for. Shortly after Star Trek was dropped, the Screen Actor's Guild came out with a clause that stated the actor must have residuals in perpetuity even if it only amounted to 25 dollars each time around. So none of us are participating in the 79 jewels for Paramount. It's all theirs. A lot of people think we've been getting paid for all these years, but we haven't. That's the very sad part of it. But things could always be worse."
Being a descendent of the original Star Trek carries with it a number of large burdens. The original has passed into folklore, and its children (like the offspring of any celebrity) have certain expectations placed upon them. Inevitably, they fail to live up to them because it's impossible to duplicate what has gone before (think Frank Sinatra, Jr.).
But that's not to say it isn't worth trying. The younger Sinatra could actually sing just fine, but he could never be his father. That's what we have here.
You might think that with 25 seasons and 624 episodes between them, the offspring have been outrageously successful. And they have -- financially. But artistically, only a tiny sliver comes anywhere close to the best of the original. Admittedly, the worst of the original also rank right down there with all the rest, but it's the best that matter.
Of the 79 original episodes, perhaps 25 qualify as really good. Of the remaining 624, about the same number qualify. It's not that 600 are bad, however. It's just that the original took great risks and hit some very high highs, and some very low lows. The formula for the other shows was established early, and real risks were few and far between. Thus the good rarely reach the heights, and the bad are always at least generally palatable (i.e. nothing in ENT is as bad as The Alternative Factor).
I want to make it clear that the people who work on these shows are the very best and they do excellent work. But their leaders have allowed the franchise to descend into formula:
1. The ship is in danger from an unknown peril.
2. The nature of the peril is finally revealed in act 5.
3. A quick fix is whipped up by the doctor/engineer/guest etc.
The dialogue is often predictable, and the situations are rarely new or interesting. The original had red shirts, but they didn't infect entire episodes or the format itself.
It's been a slippery slope, but it started with the later seasons of TNG. There was a brief reprieve in DS9, but then it was downhill in a hurry until ENT was essentially unwatchable (if you think otherwise, do yourself a favor and rent the original).
Beyond these things, the magic of the original cast was never duplicated. The sheer excitement of being out on a spaceship exploring the galaxy was gone from Picard's Enterprise, and Archer's knew only a vague "gosh, golly, isn't that neat" tingle.
These shows were competent TV, and periodically competent science fiction, but they rarely sang. That is a very great sin.
Here are some thumbnail series reviews which certainly do not claim to be exhaustive.
The Next Generation has the benefit of the best actor to ever appear associated with Trek (Patrick Stewart). But it suffers from a warm fuzziness that was a signature of its era. In some ways, TNG is what Roddenberry originally wanted for the first series (and the ill-fated Star Trek II). But he had better, more forceful editors with better ideas on the original. TNG was too self-indulgent at times, and eventually settled into the formula mentioned above. It was at its best when new writers came in and broke rules (for a while). It was at its worst when it tried to be important. Roddenberry always wanted Trek to say something, but do it through the character situations. TNG often just said things, then went off about their separate story.
Deep Space Nine actually reinvented the franchise, shaking off much of the TNG sweetness in favor of something more political and mystical. To me, it never feels directly descended from the original series, despite its canonical continuity. This is a good thing because it expanded the universe in a way which allowed more story freedom. With a mystical religion to draw upon, issues of spirituality could be referenced, and this was always used to great effect. And the move into longer storylines was handled extremely well, keeping each episode self-contained while rewarding the regular viewers. It wasn't exactly Trek, but as TV spaceship shows go, it was pretty darn great (credit Avery Brooks with setting the perfect tone).
Voyager was doomed from the moment Kate Mulgrew stepped onto the set. Her vapid captain was never written very well, but that's probably because she was so ill-suited to the role. A central premise (the maquis) was dropped too early, and the warm fuzzies were back along with a lot of ship-in-danger episodes. Despite some fine performers, the writers never got a handle on the characters, and they sunk back into types. And the resident alien character, Neelix, was essentially reduced to a mascot. In the end, the stories were mostly rehashes of rehashes, filled with automatic writing and technical solutions leading to quick fixes every week.
Enterprise, despite its promising concept, was completely dead on arrival. All of the bad things about VOY were retained, and the self-consciousness was ratcheted up a few notches until it seemed like every single episode had to have a reference to something somewhere else in the future canon. Scott Bakula seemed a good choice to play the captain, but he never got out of comic book mode (I think he has about two different looks). The rest of the characters were throw-aways. Most episodes were unwatchable, and its early cancellation was an act of mercy.