The Excelsior-class is one of my favorites. A bit wonky from a top-down view, but gorgeous from every other angle.
The Sovereign-class continues the general aesthetic of the Excelsior, but for the TNG-era design style and fixing the problem with high angle views.
The Valdore-type warbird from Nemesis is probably the best thing about that movie.
The Klingon D4 from Into Darkness is similarly one of the better things from that movie.
The NX-class Refit is also just shockingly pretty. Makes the original look incomplete.
Not canon, but I love the original “Long-boi” Discovery design. It gives off some very cool art-deco retro-futurism vibes. Not very classically “trek” but I love it nonetheless!
That is the canon design for the Discovery before the far future refit it got.
They actually did. Remember the Relativity? They talk a big game but, like the regular Prime Directive, the Temporal Prime Directive is secondary to the continued existence of the Federation. That's why there wasn't a peep out of them when Kirk stole some whales from the past.
Transporters are way less useful on their own than you think. Take the following scenario...
Centuries ago, your people developed transporters. You improved the tech until you could beam to the next star system. Now you have a network of them spanning hundreds of light years. You can cross your entire interstellar civilization in minutes. Your people discovered warp a couple decades ago, but it's merely a curiosity next to your transporters and wasn't developed much.
One day, you encounter a new alien race called the Romulans. They use primitive warp drive ships rather than transporters, so you don't think much of them. Things are a bit tense for a few years, and then they demand your unconditional submission to the Romulan Star Empire. This is absurd, so you obviously refuse.
Three days later, refugees start beaming in from one of the outer colonies. Reports indicate that none of your soldiers ever saw a Romulan. Rather than beaming down soldiers to fight, the Romulans levelled the colony with energy weapons from high orbit. Your forces tried to board the enemy ships, but they had some kind of energy field around them preventing transport. A lucky shot from a planet-side cannon firing beyond its rated range managed to find the mark, but was blocked by that same energy field just meters away from the hull.
It's been three weeks and now the Romulan fleet is in orbit of the homeworld. Bolts of green light start falling from the sky, obliterating the capital city, but leaving the capital building intact. Your transporters are still unable to pierce their shields. Your scientists think they'll crack it eventually, but they need weeks and you only have minutes.
With all the major population centers destroyed, the Romulan commander repeats their ultimatum: unconditional surrender or complete destruction. You accept their demands. Three Romulans beam into your office, the first time since the war began that your people have come face to face. Two are holding rifles. The other is holding a document and a pen.
Interestingly, this scene technically isn't part of continuity because "The Cage" as a whole technically isn't part of continuity, only the parts that made it into later episodes, like "The Menagerie," are. Remember, "The Cage" was a rejected pilot that only got released later on as a bonus, like a collection of deleted scenes. "Where No Man Has Gone Before" was the show's accepted pilot.
Common misconception. There were several different emblems for different parts of the fleet, but each ship did not have a unique emblem. Someone from the costume department assumed that each ship had a unique emblem and one episode had it wrong, but we also have the memo telling them to not do that again.
I've heard that Data was originally going to be a science officer and the blue uniform didn't work with his makeup, but I don't know whether or not it was true.
I'm pretty sure he was also the only command division officer on the bridge after they gave him command. At least in theory, due to differences in training, a lieutenant jg from the command track may be better suited for acting captaincy than a full lieutenant from science, especially with a decidedly non-sciency mission like flinging a warship at a wall. You need that dash of crazy that Starfleet's command officers tend to have.
Voyager had phasers on the pylons. The Enterprise-D actually got phasers added to the nacelles, of all thing, in a later season. I don't think either ship was actually seen firing them, though.
That's clearly a yellow beam, making Worf a Jedi Sentinel.