This was George Lucas' first film, and it's more or less unheard of. It's brilliant! It has a real subdued and contemplative feel to it, and some fairly intense moments. Stylistically, it feels somewhat similar to Star Wars, so it's worth a watch if you're a SW fan. The ending is just amazing; I shan't say any more than that, but it's worth watching the entire film just for the final 5 minutes.
The World, The Flesh and the Devil - One of my favourite movies. I think I love everything about this, even the grating hairdressing scene. Some of the plot points that guide this film are contrived, yes, but it's a character piece first and foremost.
The War Game - A short what-if documentary based on scientific fact mixed in with some realistic assumptions based on other bombings.
Things to Come - It's not perfect, but some of the ideas and sets are well realised. My favourite part is the mid-section where Everytown is less a town, more a military outpost and the disease sweeping the world has created zombies wanting to infect the healthy. They really should have expanded that.
On The Beach - I haven't watched either version yet, but they do seem pretty good. 5ive - I haven't watched this either, but it also seems like something worthy of looking into.
The Day After and Threads - Both of these films follow a bunch of characters before and after a nuclear strike. Threads is much more grim and realistic and is a lot slower in pace.
A Boy and His Dog - A fun movie about a boy and his dog and mans animalistic tendencies.
The Last Man On Earth - A very good film with Vincent Price. He lives alone in a world of mutants and then he finds another survivor which challenges his perceptions.
And last but not least is an interesting Czech film called Konec srpna v hotelu Ozon (Late August at the Hotel August) and its about of female nomads led by an old woman who was born before the nuclear holocaust that destroyed the world. Animals were harmed during the making of this film.
I'd second the mention of 12 Monkeys, and throw in The Quiet Earth, a fairly rare film. And this is sort of borderline, really, and probably doesn't belong here, but Miracle Mile for sheer originality.
Well, the premise of Miracle Mile is far stronger than the reality, but it tries. I'll give it brownie points for that. Plus, I have a history with this movie. I narrowly avoided being struck by lightning during the grand finale.
In the sense that it took a while to appear on DVD and is never shown on cable, that I know of. So" I meant "rare" in the sense that it's something you'd really have to know about already to see; you won't stumble across it by accident...