I always really liked "28 Days Later". Now I know it wasn't really an apocolypse or end of the world, as the infection only spread through what seemed like most of the UK or perhapes just England, but the rest of the world was fine.
What was interesting is you didn't know that through the movie and more important, THEY didn't know that. They thought the world was fucked and they were some of the only survivors. I loved the way that movie was filmed and I felt it was very true to how an end of days might seem for a lonely survivor. The reasons weren't very absurd and the characters felt real. It seemed like a likely scenario that could possibly happen.
"The Day After" is another great one. I saw this for the first time when I was pretty young and it scared the living shit out of me. It is about a nuclear attack and how a small town and a few farms in Kansas USA deal with the after math of it all. It was very gritty as you watched many of them die of radiation poison, starvation and thirst. Still not really a "End of the world" movie, it showed a very real situation that we as humans could find ourselves in.
Then there is probably one of the scarriest movies I have ever seen, "Outbreak". This movie gave me nightmares as a child when I first saw this. It is about a viral outbreak of a disease much like ebola. A monkey is host to a disease as he is illegally brought into america, when the monkey scratches the man he gets infected. Then he infects his girlfriend and a petstore owner that he tries to sell the monkey too. So one by one an outbreak happens. This is a very real scenario and great film. Not to mention how the government/military respond to containing this disease. -SPOILER-, The virus is dealt with by the end of the movie and the world does not perish, so like the other two, this isn't really a end of the world movie.
I suppose movies like Omega Man/I am Legend, The Day After Tomorrow, Children of Men and The Road are good movies and everything, some even great movies, but they don't feel like they could happen as likely as one of the others I mentioned. And don't even get me started on that crap "2012" movie.
I always found dying of some Infection/Disease was the worse way to go, as it attacks and effects YOU as a being, instead of just a quick and climatic death. It prolongs your death and makes you suffer. Whether it's Radiation posion like in The Day After, Eboli type virus in Outbreak, or a Rabies type virus in 28 Days Later.
28 Days Later - 2002
The Day After - 1983
Outbreak - 1995