Inspired by this thread.. 
Martians, xenomorphs, and an assortment of extraterrestrial horn-dogs have been chasing earth girls for decades.
[Professor]For the love of god, why?[/Professor]
Why do some men have sex with sheep? They’re available.
Bexause it appeals to SF readers, of course. Mostly male-type readers who can identify with whatever hero is there.
Rest asured, SF writers and magazines have been poking fun at this (and other sexy and sexist) story cliches for ages. Asimov wrote a story about it for Playboy (which they never published). Fredric Brown did it back in the early 50s in “What Made Universe”. et cetera.
My favorite one-line criticism of the entire idea, though, comes from Larry niven’s “Man of Steel, Woman of Kleenex”:
“On the face of it, Superman could as easily mate with an ear of corn.”
(Of course, there have been more sophisticated attempts to mix SF and sex. Read Philip Jose Farmer’s “The Lovers”, for instance.)
Movies in which Aliens Need to Kidnap our Women:
Mars Needs Women (Natch! With Tommy Kirk as the lead Martian)
**Frankenstein Vs. the Space Monster
The Mysterians
Pajama Party** (!! With Tommy Kirk as the Martian again!)
Queen of Outer Space
Does Mars need women? Of course not! ** [Mars Needs Guitars/B]!
A great album, BTW.
Earth Women are Easy.
Dammit! The “Luxury Cruises to Mars” ad at the bottom is a dead link! 
Depends on what needs we’re talking about.
For example in War of the Worlds Women and for that matter men were merely foodstuff. In Mars Needs Women it was mainly due to the lack of Martian women about. Some sort of disease or something (probably picked up when they tried to invade and caught colds)
Invaders from mars was different… they didn’t want just women they wanted men too. These folks used as automaton slaves to sabotage our rocket program!!
Pesky Martians… always wanting … always using
No, no, no!
The man from mars is eatin’ cars. And when he’s through with cars he’s eatin’ bars.
(Rest assured, however, now the man from mars stopped eatin’ cars and eatin’ bars. Now he only eats guitars.)
Women are yummy! 
The reason is simple. Men’s body hair tends to get stuck between their teeth, and men are generally tougher and stringier. Once you bite the head off women don’t have as much irritating hair, and are chewy without being tough.
You beat me to it, I was going to say that. 
I can’t imagine why, all things considered.
I note a distinct lack of . . . ummm . . . orfices of any kind. There’s something Earth women have over Martian ladies right there.
Though the creatures are not extraterrestrial, here’s an honorable mention for Humanoids from the Deep.
Mars’ Agenda:
Step 1: better atmosphere for breathing
Step 2: women
Step 3: profit !
There was even an explanatory line:
HOT BLONDE CHICK SCIENTIST: I believe they’re driven to mate with humans to advance their evolution!
As a Scientist, I believe it’s the boobies.