My top one is Berserk by Kentaro Miura. Not quite a "true" apocalyptic themed anime. I must admit that I only watched the series and have yet neglected to read the manga.
Set in an European medieval time, the TV series with the exception of the first episode is a recap on the main character Gattsu(Guts). The series shows Gattsu's progression from a boy to a man who can wield a humongous sword. The series finally gets dark and shows how Gattsu's (personal) world changes as all his friends are sacrificed.
Apparently, the manga covers quite a bit more. There is a lot more blood and violence too.
Neon Genesis Evangelion
Texhnolyze
Casshern Sins
Cowboy Bebop
Blue Gender
Akira
Roughly in order.
"Why did he have to surrender, what is more in the outside world, huh, sumptuousness, freedom? Nowhere in the world are you going to find them fools! Fools!" -USSR president, Future War 198X-nen
Akira - Both the manga and the anime are awesome.
Appleseed - Haven't seen the anime yet, but the manga is pretty good.
BLAME! - Really interesting, and it has a great setting.
Devilman - One of my favorite manga, it's really amazing. Only the last few volumes are post-apocalyptic though.
Fist of the North Star - The anime and manga are both good, but the manga is much better. Also, you are already dead.
Future Boy Conan - A great early Miyazaki show, gorgeous animation, and it's got a lot of stuff in it that ends up in later Ghibli movies.
Hotel - The title story is a fantastic story about a robot that becomes sentient after the fall of mankind.
Nausicaä of the Valley of the Wind - Another great Miyazaki movie/manga.
Riki-oh - It's like Fist of the North Star, but with more crazy-awesomeness.
Trigun - DEEP SPACE PLANET FUTURE GUN ACTION!!
Violence Jack - Sequel to Devilman, and like Fist of the North Star, but with a lot more gore.
Kiba no Tabishounin - The Arms Peddler : A post apocalypse world with a somewhat homestead feel. A boy (Sona Yuki) and his family are attacked and he is left to survive after being branded. Just as he is about to give up on life and die, an arms merchant sells him a knife in exchange for his servitude. Now, Sona must travel from town to town and seeing how dark human nature can be.