On the NCC-1701 (The A team)
-Captain: James T. Kirk
A cultural icon who's a renowned explorer, has won countless ship-to-ship and hand-to-hand battles with more beings than anyone else (not to mention his getting off with more gals than anyone else in the galaxy.) Cares about his crew and the well-being of all above all.
-Second-in-Command: Spock
He's Spock. EVERYONE knows Spock- enough said.
-Engineer: Montgomery "Scotty" Scott
Another cultural touchtone, one of the most famous Scottish (even if he really wasn't) characters in media history. Not ONLY has he repaired and improved every spaceship he's ever touched, but he's done it, gotten drunk, then done it with a hangover :p THAT's talent.......
Doctor (Medical): Leonard "Bones" McCoy
If you've ever heard "Damnit Jim, I'm an doctor, not a ____" or "He's dead Jim!" in a skit and not known where the joke came from, look no further. More than a doctor, McCoy serves as the emotional Yang to Spock's logical Yin, giving the middle-ground Kirk the full picture and making him unbeatable when the three of them are together.
Helmsman: Data
If you were expecting Sulu, sorry- they can't ALL be TOS, and Data is superior in any case. an android that wants to be human, and reminds us what it is to be human, Data is one of the most intriguing characters in Trek, blessed with superhuman-level intelligence, comprehension, reflexes, and strength, plus an ever-increasing ability to "be human," Data is also now a member of the Robot/Android Hall of Fame. And he pilots the ship pretty well, too. :p
Navigation/Weapons: Worf
Along with Data, one of those characters on TNG that allows you, the audience, to see humanity from the view of an outsider, Worf is a Klingon among humans,a warrior in anti-war Starfleet. He brings a much-needed touch of agression to Picard ans Sisko's ships (and then Picard again in the movies) while always retaining a sense of dignity and honor. Worf is easily the most trigger-happy character in our pantheon of heroes here, and has the most extensive weapon knowledge.
-"Nurse": Deanna Troi
Technically a counselor and shrink, Troi is the moral conscience of the crew of Picard's ship when even the most merciful crewmembers are howling for blood. ALWAYS trying to see every conflict from every angle, Troi also gets bonus points here for being a telepath of sorts.
-Auxillary Crewmember: Seven of Nine
Even ignoring the admittedly shallow reasons for wanting to put Seven into a fight, she's easily the best non-traditional-post character in any series. Technically human, she's still partially Borg, and thus keeps all that tenacity and efficiency.
NCC-1701 D (The B team)
-Captain: Jean-Luc Picard
Whether he or Kirk is the better captain (I personally like bothe but favor Picard a touch), there is no doubt Picard's another cultural icon and great leader. Where Kirk relied on his guns, guts, his crew to do their job and Spock and McCoy's advice, Picard is more of the thinking man's captain, and the ultimate delegator of duty; he ALWAYS gets the right people in the right place at the right time to do just the right thing (and he had the courage to go into space bald lol.)
-Second-in-Command: William T. Riker
Whereas Kirk's the more emotional and Spock's more logical, Picard and Riker are the reverse; they don't have the same chemistry one on one, but rather Picard lets Riker develop into a far different captain than himself.
-Engineer: Geordi LaForge
If you're a DS9 fan and hate O'Brien's not here, sit tight for a bit. Geordi, meanwhile, has superior (in some ways) sight than others thanks to his VISOR, and was given the blessing of the master, Soctty (and Scotty wasn't even drunk......) In any case, Geordi's pulled his Enterprise out of plenty of harrowing experiences, too.
-Doctor: "The Emergency Medical Hologram" (EMH)
Another of the want-to-be-more-human characters, the EMH is a hologram that has a VERY useful feature- since he's tied in with the ship, he can (eventually by the end of the series) go anywhere in the ship in a second, and is less vulnerable to attack, let alone his computer knowledge of medicine.
-Hemlsman: Hikaru Sulu
Here's Sulu. The eccentric and "flamboyant" helmsman on TOS, Sulu is one of the best pilots in the fleet, can lead a landing pary, eventually becomes captain of his own ship, and is a great hand-to hand/melee fighter (fencing, anyone?)
-Navigator/Weapons Officer: Pavel Chekov
I have an admitted bias here- Chekov is my favorite character in all of Trek, why is another story. Worf served on TNG-DS9, and Malcolm Reed on ENT is really forgettable and nothing special. The only serious competition here are Harry Kim and Tuvok, both from VOY. NEITHER are as versatile as Chekov, however- Chekov is constantly gaining experience and strength, takes more punishment than any non-red shirt, can take an active role in landing parties, and can navigate and fire phasers and photons well, and at the same time.
-"Nurse": Nurse Christine Chapel
There really aren't too many big roles for Trek nurses (the Doctors get all the glory) so Chapel gets the nod for being competent and the only Trek nurse who was actually........ a nurse.
-Auxilliary Crewmember: Miles O'Brien
See, DS9 fans, here's your Irish techie. Another great engineer, O'Brien probably also saw the most sombat and leadership action of any non-captain or second-in-command character (though Scotty and a couple others can have an argument at that.) Whatever the case, O'Brien is extemely versatile in battle and in the engineering room, and is the pick here.
So that's the Sweet 16 for Trek: Doctor Who fans, your turn......