Nastassja Kinski is Irena, a waifish virgin who has been tracked down by her creepy brother Paul (Malcolm McDowell - does he ever not play creepy?) and brought to New Orleans. Their parents died when they were young; the siblings were separated and only recently reunited. The other thing about Irena and Paul is that they are Cat People: they can only have sex with each other or else they turn into black leopards post-coitus. They have to stay in big-cat form until they manage to kill someone and then they can change back. Paul is hip to the situation; Irena is just figuring out the horror movie trope of once you have sex, bad things happen to you.
John Heard (Oliver), Annette O'Toole (Alice) and Ed Begley Jr. all play zookeepers. They get involved after Paul shags a hooker and turns into a leopard; the zookeepers manage to capture him for a while. Now, I would like credit for this prognostication: about one-third of the way through the movie, after Paul-the-leopard has been brought back to the zoo, and as Ed Begley Jr. was attempting to clean the big cat cages, I announced to anyone who was listening (the dog, Mr. Mouse having gone to bed), that Ed Begley Jr. would be killed by the leopard. Lo and behold, within twenty seconds of my pronouncement, the leopard had ripped Ed Begley Jr.'s arm off and the poor fellow bled to death.
Sidebar: For a horror movie, there's very little gore - the disarming (heh) of Ed Begley Jr. is the most of it, with a couple of scratchings, a body wrapped in a bloody sheet, some gooey stuff and an autopsy of a Cat Person in leopard form. I understand that you don't have to have a lot of blood and guts in a horror film, but if that's the route you're going, you have to ramp up the suspense and atmosphere, throw some scares in that way. Cat People is nearly bereft of such atmosphere, unfortunately.
Long story short (and it's really not much of a coherent story with jumps and gaps and leaps of logic), Irena tries to be a good girl but when her brother is killed she embraces her feline-icity and eventually has sex with Oliver. This sexual awakening literally releases the beast within. However, when Irena morphs into her leopard-form, she is unable to kill the zookeeper because she loves him. So she runs off and kills someone else in order to get back to human form. Realizing that if she wants to be with Oliver she can never again "be with Oliver" without consequences, Irena finds her lover and asks him to "free" her. He's down with it, but first ties her to the bed (fun with bondage!) so she can't maul him after they do the nasty. The final scene is actually kind of sweet: Oliver goes out to the big cat cages at the zoo and hand-feeds a beautiful black leopard. She purrs and he skritches her behind the ears. I can't read the name placard on her cage but I'm guessing "Irena" would be too obvious.
There is a fair bit of nudity in this movie: Kinski gets fully naked a lot, both McDowell and Heard flash their tushes and Annette O'Toole (Mrs. Kent from Smallville!) goes topless. Everyone looks great and it was fantastic to see all-natural boobs for a change. Yay for the early '80s!
The absolute low point is a dream sequence in which Irena learns the history and/or mythology of the Cat People. It's all gauzy scarves, wind and fog machines a la an excruciating music video. Boo for the early '80s!
And finally, big points go to Mr. Mouse who, before he went off to bed, correctly identified the Cat People theme as being performed by David Bowie - before any lyrics were actually uttered! Very impressive.