Here is one opinion on this:
And finally, sometimes the absence of “The” gives a movie title an unsettling aura. It doesn’t sound wrong, but it feels like there’s something missing or just a little off-kilter about it.
Psycho, Alien, Aliens, Predator, Blade Runner, Gladiator
Without “The,” none of these titles point to a definitive subject. They become rather subjective and even more fascinating as we explore their full implications as the story unfolds.
(from 'The Huge Impact of ‘The’ in Movie Titles')
But not everyone agrees (though I admit I'm not 100% positive this piece isn't tounge-in-cheek):
Wouldn’t almost every movie title be better with The? The Raging Bull? The Citizen Kane? The Rebel Without a Cause? The Alien, The Aliens, and The Alien3? Shouldn’t George Lucas have gone with his original instincts and called it The Star Wars?
(from 'The 'the' is THE best thing to happen to the titles of the movies in the theaters')
In general, the quality that is conveyed by omitting the article is kind of elusive and hard to describe. Consider the following attempt, in the context of titles of paintings:
Japanese Vase - a Japanese vase chosen at random from many examples probably because (i) it was convenient and/or (ii) it appealed to the artist.
A Japanese Vase - An example, probably typical, taken from many Japanese vases.
The Japanese Vase - (i) the definitive example of vase of Japanese origin or (ii) the Japanese vase that is associated with some commonly known event/person/history/style/etc. (iia) used where the painting is really famous: "The Mona Lisa" "The Sunflowers" "The portrait of Whistler's Mother."
The contrast between the A and The versions is clear enough, but I'm not sure I would understand, from this description, what the difference between no article and the indefinite article is supposed to be.
In some specific cases, the impact of including or excluding the article can be given an interesting analysis. The following passage makes a comparison between the titles of the movies The Wild One and Wild Hogs, specifically as far as what effect the incusion or exclusion of the article has on them:
The title of the film likewise performs work of cultural containment when read against its precursory text. Like many narratives of heroism and anti-heroism, The Wild One instantiates the exceptional—indeed, marginal—masculinity of a single member, Johnny Strabler, among a group of men, a trope in narrative evident since Gilgamesh and the Odyssey, and extant in American culture from James Fennimore Cooper’s novel The Deerslayer (1841), to Michael Cimino’s film The Deerhunter (1978), and beyond. In the case of Benedek’s film, the plural title, lacking a definite article, emphasizes the corporate community of identity in the non-gang relations of the four Wild Hogs, each supporting one another, yet not within a hypermasculinated group, such as a motorcycle gang, so that each is not code-bound to prioritize the group over the self, and is therefore free to pursue his own pursuits, while maintaining membership. It is significant then that when Damien Blade asks the Hogs, “What do you call yourselves?” they answer initially by giving their first names, so that Blade reformulates the question to elicit their group identity as “Wild Hogs.” The non-gang’s interrelations emphasize somewhat fluid and empathic masculine identities, as opposed to the comically flattened characters and more strictly stratified relations of the “real” motorcycle gang, whose stereotyped identities signal their outmoded masculinity, replete with clubhouse/bar, ape-hangers and loud pipes, coercion, and threat of violence. And as we will see, a latent impulse of homosexual violence erupts from gang member Red, only to be slugged into silence by Blade.
(source, boldfaced emphasis mine)
Specifically in the case of Alien, in the The Book Of Alien, the way the title came about is described as follows:
The working title was Star Beast. O’Bannon had a fortunate brainstorm late one night as he continued to write while Shusett slept. “I was writing dialogue and one of the characters said, ‘What are we going to do about the alien?’ The word came out of the page at me and I said, ‘Alien. It’s a noun and an adjective.’ So I went in the other room and shook Ron awake and told him and he said, ‘Yeah, OK,’ and went back to sleep. But I knew I had found a really hot title.”
It is true that leaving out the article was necessary to make alien function as both a noun and an adjective, but that clearly isn't the only reason why the article was omitted: after all, the working title, Star Beast, was itself a noun phrase that was missing an article.
For what it's worth, there is at least one aspect of the articles in the titles that can be explained pretty well. The following is a relevant section from Collins COBUILD English Guides: Articles (p. 34); the usage in titles of novels etc. is mentioned at the end:
4.13 Using the definite article at the beginning of
Consider this sentence, which is the first line of 'The Catbird Seat' by James Thurber.
Mr Martin bought the pack of Camels on Monday night.
Why 'the pack'? It would be perfectly normal to say 'a pack of Camels' (a brand of cigarette), especially as the reader has not been told anything about it before. The answer is that the writer is indicating in this way that the reader will shortly be told more about the pack. Here is another example, from the beginning of 'The Lord of the Flies' by William Golding:
The boy with fair hair lowered himself down the last few feet of rock and began to pick his way towards the lagoon.
The boy and the lagoon have not previously been mentioned. It is only later that the reader learns more about the boy, where he is, and why he is there.
This is a stylistic device which you probably will not need to use, but you will need to understand it. Titles of stories and novels are similar: 'The Catbird Seat', 'The Man Who Knew How', 'The Letter', 'The Enemy', and so on.