in typical Star Trek fashion, it's heroic to question these matters
I absolutely love this series, even the bad ones. With the exception of The Undiscovered Country, all of these are currently streaming on Netflix. I'm not sure if they're a good point to jump on for potential fans, but you could do worse on a Saturday night than having an original Star Trek movie marathon.
In chronological order:
Star Trek: The Motion Picture
This one I love to hate. Well, hate is a strong word. A few years ago I saw the director's cut and reviewed it here. I don't care who you are, you'll like the sequel so it's worth sitting through this one even if you fall asleep... like I did.
The Wrath of Kahn
The Hollywood-level of action and conflict is cranked up to eleven in this one. Even so, it manages not to become bloated while retaining a lot of the stuff hardcore fans like. It's a surprisingly effective action movie. Although it's the fan favorite, it's actually my least favorite of the even-numbered films.
The Search for Spock
In case you haven't seen The Wrath of Kahn yet, I won't spoil where Spock is. The way they find Spock is a lot less magical than you expect, even if the science is stretched a bit thin. In this one, something happens that really cements Kirk's hatred for Klingons. That'll come around and bite him in the ass a few sequels later (The Undiscovered Country). It goes to show Star Trek has the potential to be a lot better when it has a less episodic story arc. I love Christopher Lloyd as a Klingon, but watching a younger version of Spock experience pon farr (links to the only episode of Enterprise I've ever seen) was pretty disturbing. The climactic battle is pretty unbelievable—not in the good way.
The Voyage Home
I think this is the first Star Trek anything I ever watched (I was three when it came out). All these years I thought there was no way I could possibly like it as an adult, but when I saw it again I fell in love with it. I typically hate comedies like this and it's very much a comedy. As is such it's the most bizarre Star Trek film ever made (see Spock spouting pseudo-obscenities). Even though the reboot series is borrowing heavily from this series' sequence of plots, there's no way in hell they'll borrow from this film. There's simply no way a movie like this can be made today, especially with a big-budget franchise. Although it's the film anyone can like, the effectiveness is much greater when you're familiar with everything that came before it. The hilarity of these characters being thrust into this situation will be lost on people unfamiliar with their typical personalities.
The Final Frontier
The Final Nightmare, The Final Friday, The Last Crusade... yeah right. Whereas the previous two films in the series were directed by Leonard Nimoy, this one's directed by William Shatner. If ever you needed proof of Shatner's ego, he opens the film on himself, bloated and about a hundred years old, climbing a mountain without any gear whatsoever. You know you're in trouble the second you see Spock levitate on jet boots. Look, there's a lot of shit in this one (it's easily the worst of the original films), but like I said above, it's got one of the best lines in movie history. Although the special effects took a hilarious downturn in quality, the film as a whole is not as bad as people claim.
The Undiscovered Country
This is easily the most well-rounded of everything we've seen prior to it. Ultra-serious actor Christopher Plummer makes a great Klingon. I must confess to having had a massive, prepubescent crush on Kim Cattrall's Vulcan character when this premiered on HBO. David Warner, who was in the last film, comes back as a short-lived Klingon who's attempting to orchestrate peace between his race and Starfleet. Unfortunately Kirk, who's experience all the way back in part III continues to make him despise Klingons, finds himself in the role of ambassador. Like The Wrath of Kahn (which this film seems modeled on, right down to the choice of director), it's an intense action flick which should have made a lot more money than it did. It's a close tie with The Voyage Home in terms of which Star Trek film is my favorite.
I haven't seen this one since it came out and don't remember much aside from the "surprise ending" that was one of Hollywood's worst-kept secrets. I liked it at the time, but that's all I can reasonably recall. I'm not sure I'd call it one of the originals, though, so I'll look into it more deeply when I review The Next Generation films.