The fans of Star Trek know and have studied a lot of things about the franchise, but I think another look at the characters that've populated its five casts can still break new ground.
(the original series, animated series, the first seven films, and the 2009 reboot)
Starting things off with the first cast and the one that's still the most famous, we have three obviously very prominent main characters in James T. Kirk, Spock, and Leonard "Bones" McCoy. There's little dispute that these guys received the bulk of the material, very consistently. Spock is the only character to appear in both the original pilot ("The Cage") and the subsequent Kirk adventures that followed. While the style of the original episodes is different from the rest of the franchise, in that very rarely was a story built around a character so much as the characters experienced events (though these episodes heavily populate later incarnations as well), with notable exceptions like "Amok Time," the three seasons of the original series plainly utilized memorable personalities in each of the characters, who were all good friends (a point that might need reminding between Spock and McCoy). Scotty was always the fourth lead, after all being a "miracle worker" who was the direct conduit to the starship Enterprise's inner workings. Sulu, Chekov and Uhura each had memorable parts to play as well, with Chekov coming in fifth, Sulu sixth and Uhura seventh as far as overall importance goes. Nothing much changed in the animated series, and by the start of the movies, some of the smaller parts started to expand a little. Sulu was meant to have his first command in the second film (only George Takei and his supporters will ever be able to properly explain the injustice of William Shatner's implicit veto of that call), but got it in the sixth. Kirk had a prominent part in the seventh movie, with Chekov and Scotty tagging along for a brief moment. I think only in the 2009 reboot did the best dynamics truly work themselves out. Kirk and Spock were left in the spotlight, McCoy stole all of his scenes, Uhura took fourth lead, Scotty fifth (small demotion!), with Chekov and Sulu picking up scraps.
The Next Generation
(including four films)
Launched in much the same vein as the original series, the new batch of characters were nonetheless on fairly equal footing aside from Jean-Luc Picard and Data. As the series progressed, other characters grew in prominence, notably Worf, though everyone had a chance to shine in some capacity, with a rough breakdown of Riker in fourth, Troi in fifth, La Forge in sixth, Beverly Crusher in seventh, Wesley Crusher in eighth (if he'd stayed on longer than he did, the rank would be higher), Pulaski in ninth, Yar in tenth (she left because of this treatment, by the way). While Data and Worf received the bulk of personal growth, Picard had a few key moments, notably everything that followed his assimilation by the Borg, including the film First Contact, and Riker and Troi finally completed Star Trek's first successful romance in Nemesis. On the whole, however, characters remained secondary to their adventures.
Deep Space Nine
Famously the Star Trek with the most in-depth look at its own landscape, including an abundance of supporting characters, this series had a rough start in that regard, though the ones that received the most treatment early on remained the ones who got the most consistent treatment later: Kira Nerys, Odo, and Quark. Sisko had a strong early push in the first episode, and a strong later push, but it took until the third season for anyone to truly know what to do with him. It still puts him in a comfortable fourth place, the lowest rank for a captain so far. In fifth and sixth come Bashir and Dax (including both incarnations), who were both portrayed as young characters early on with much to learn, even if one of them didn't want to admit it (Dax learned better in the second season). O'Brien was the steady rock DS9 stole from Next Generation, and probably wouldn't begrudge seventh in such a strong cast. Most of his development was learning to be comfortable in his new setting, and by the end of it, he happily left the station (anyone else ever note the irony of that?). Jake Sisko comes in ninth for being used sparingly, but still ahead of Worf in tenth, who never truly seemed comfortable. I could then list the thousands of other characters, and probably start with Dukat in eleventh, Garak in twelfth, Winn in thirteenth, Nog in fourteenth...You see how many characters there were? And they were all important to the story, because the characters were the story.
Repeatedly knocked by its vocal detractors as nothing but a poor man's Next Generation, that's extremely hard to defend when you look at it from the vantage point of its characters, who consistently behaved a lot more like Deep Space Nine's. In fact, Voyager was exactly like DS9 in a starship setting. The characters were king. Kathryn Janeway especially. From the first episode it was clear that she was in command. The divisions behind her get a little complicated. Seven of Nine, introduced in the fourth season, will always vie with the subject of one of her most complicated relationships, the Emergency Medical Hologram ("The Doctor" to his friends) for second. Tom Paris and B'Elanna Torres similarly, appropriately, battle for the next spot. Neelix takes the one after that. Chakotay, Harry, and Kes fight over the remaining spots. You see how it's tricky? Things were always changing on this show. Chakotay was indisputably in the second spot early on, but in the third season his role became a clear supporting one, as the series began to use the original series approach. Kes was sporadically important, but left after the third season. Harry was very clearly a classic Sulu/Chekov/Uhura figure, but he had bigger moments than they've ever gotten. The characters almost always defined the nature of the problems face in any given episode, even if by definition couldn't have their own stories told, given that home was a long way off. Seven and Chakotay cheated this rule on a few occasions, and so will always have special designations (and not just because one of them used to be a Borg!), while Kes lived it but didn't get to properly finish her journey (though examining what she actually did accomplish will always be fascinating). The final episode focuses, naturally, on Janeway.
Taking things that were learned on Deep Space Nine and Voyager and applying it to the original series formula, the most recent new cast was led very deliberately by a trio of characters: Jonathan Archer, Charles "Trip Tucker III, and T'Pol. Phlox would come in fourth, Reed in fifth, Hoshi in sixth, Mayweather in seventh (Shran in eighth! Soval in ninth! Daniels in tenth! Silik in eleventh! Forrest in twelfth!). Yes, Mayweather was very clearly cut from the Sulu/Uhura model, but like Harry Kim received a lot more spotlight moments, coming from a mindset that more closely resembles Kira than Chekov. It's unfortunate that so many fans chose to overlook this about the show, because characters were probably the most important in this series, out of all the incarnations of Star Trek. They defined exactly what was supposed to be happening, just as in DS9, and they were always in control of the story, even when they were simply reacting to events around them, even moreso than Janeway. It wasn't just the endless times Archer was said to be helping found the Federation, but how he conducted himself as he did it, the decisions he made, or how T'Pol pioneered friendly Vulcan-human relations (which to the show's credit fits entirely in line with the lack of progress a hundred years later when Spock is still the lone Vulcan in Starfleet), or how Trip embodied real human vulnerability and potential.
For me, how Star Trek uses its characters has always been essential to its success, no matter how it was done. The grand adventures, big ideas, and alien cultures are fine, but they would mean nothing if I had no connection to them, and that connection comes from the characters. From James T. Kirk to Charles "Trip" Tucker, the connection has remained strong, even if it hasn't always been possible to give every character their due. The ones that connect do so strongly, and that has always been the case. The role of overall characterization has changed and expanded over the years, become ever more integral to each new series and incarnation, and it's important to acknowledge that fact. It's only fitting that one of the characters who started it all was such a standout element of the 2009 film. After all, what would Star Trek be without Spock? And that's really all you need to know.