Kirk beats Superman. He asks “Why would Superman need a starship?” and Kal-El’s head would explode.
Naw. He already knows what Professor X looks like. TNG had an X-men crossover, too, this time both in a Marvel comic and in an officially licensed Star Trek book. This makes it a sort of second tier canon, similar to the Star Wars Expanded Universe. It won’t be recognized on film or TV, but it can be in books. And since there are no more of the former for this universe…
At one point I thought any superhuman immune or sufficiently resistant to hand phasers on kill could take Enterprise, but I was thinking of Borg shields, not the Federation. The former do not stop projectiles, while the latter do.
Also, you probably don’t mean Archer’s Enterprise…
Enterprise vs. Superman:
Scotty calibrates the sensors to scan him.
McCoy examines the sensor report and deduces that he is vulnerable to kryptonite.
Spock synthesizes kryptonite.
End of.
Two words:
The Spectre
He’s the actual Wrath of God. As such. God. None of this “We’re all gods in our OWN way” new-agey stuff, the Wrath of God from the Old Testament. There’s no possible way the Enterprise or a Super Star Destroyer could win. (And he’s not a one-off character. I think if you count the issues, he’s had more issues published in books solely devoted to him than The Silver Surfer has.)
We saw Phoenix take out an Enterprise analog back around Uncanny 107 (or was it the second story arc around 133?). Phoenix would be eaten for breakfast by The Spectre.
Galactus has been shown casually destroying Sh’iar ships (again, Enterprise analogs) and Dr Strange once took Galactus down in about 2 panels, so Doc Strange could beat the Enterprise.
It’s just not a fair contest unless you get rid of all the tough (Superman class), mystic, psychic and cosmic characters. Which leaves…like…um…Iron Man. And my money is still on him unless Scotty is the engineer of the ship he’s up against.
Superman flies faster than light.
Superman flies through the Enterprise faster than Kirk can say “Scotty, scan that alien”.
The Enterprise is a rapidly expanding cloud of plasma.
End of.
Actually, I’m not sure how that fight (assuming out-of-control, elemental Dark Phoenix) would go down. The Spectre is a badass but he has been pwned in the past by sufficiently powerful supernatural force (the big black hand in the post-Crisis (first one) Alan Moore Swamp Thing storyline).
Depends on whether the writer was making the point “The Spectre is the ultimate badass and even your elemental force of nature powers don’t really measure up” or “the Phoenix Force is elemental, basic, and so powerful that even the Spectre can’t contain it,” both of which are more-or-less defensible.
Wesley Crusher could kick both their…
…oh wait.
All true, but the only things that have ever kicked the Spectre’s ass is (as you said) a sufficiently powerful supernatural force.
Which the Enterprise simply doesn’t have. Even if you allow that Trelane/The Q/Whoever are magic and not “sufficiently advanced tech” (which they’ve been established as), they’re still not nearly in the Primal Darkness or Eclipso or that Indian/Devil guy (Shaitan?) category. Hell, The Anti-Monitor was barely able to battle the Spectre to a standstill and assuming he’s tech (which I’m not sure I buy), the Anti-Monitor could trash the Enterprise without trying.
Post-Crisis Superman doesn’t fly faster than light, but the current version would own the Enterprise anyway.
Well, maybe not the Enterprise-D. As soon as he battered her shields down, which I’m confident he could do, he’d x-ray the joint and be taken aback by all the civilians, which would might give Picard & Company a chance to talk. It’s hard to imagine there ever being a fight between the two, though, because neither Picard nor Superman is inclined to throw the first punch. Either would say, “Let’s talk through this to avoid any violence,” prompting the other to say, “Works for me.”
Season 1 Picard would surrender pretty quickly anyway. Hell, he did it in the series premiere!
Kirk is a superhero, to all intents and purposes. So, we have a superhero who also has a powerful starship against some superhero who doesn’t. Kirk wins.
Hmm. Assuming Superman is not a fictional character in the TrekVerse (and thus not listed in the library computer database), I think Picard would be apt to assume the godlike humanoid flying at near-warp speed without a spacesuit was half Q.
Jim Kirk vs. The Black Canary. I think we can all see where that would go.
Let’s just skip to the inevitable conclusion of this sort of reasoning any time it shows up, and all agree that Squirrel Girl would totally pwn the Enterprise (no matter which letter it has after its number).
Well, he is French. 
So. Squirrel Girl vs. Teela Brown.
Squirrel Girl.
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I buy the theory that Teela did NOT have the gene or had the weakest version of it. The “lucky” ones were the folks who broke their legs skiing, or were on vacation or whatever when Nessus came a’calling. Those were the ones who got to pass on their genes–Teela became a Protector which is a dead-end.
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Teela is super-duper annoying and whiney while Squirrel-Girl is cute as a bug’s nose. Cute beats annoying any day of the week.
Q: Why are French streets lined with trees?
A: So German troops can march in the shade.
OK, then: Mr. Rogers vs. Squirrel Girl.
And Fenris (haven’t seen you around lately), I agree with you about Teela. “Lucky”, in an evolutionary context, must mean “passes on genes”. Which Teela didn’t do.
I don’t know how much Thor you’ve read but the Marvel comics Thor would utterly destroy the Enterprise. He’s sort of a fleet destroyer. Really, he could probably take down the Death Star much less te Enterprise. It wouldn’t be close.
I think Superman would be the one major hero that the Enterprise could take down pretty easily. Sure, he’s incredibly strong and tough, but he’s essentially powered by crappy pseudo-science, and crappy pseudo-science is Star Trek’s stock in trade. I figure it would go something like this:
Spock: Captain, our scanners indicate that the individual’s body is super-charged with yellow sunlight particles.
Kirk: Yellow sun, huh? Bones, what can we do with that?
Bones: Any first year med student knows that yellow sun particles can be counter-acted by red sun particles.
Kirk: Good! Scotty, modify the phasers to emit red sun particles. Fire on my mark!
And that’s the end of the fight.