#5 - Grave of the Fireflies: Quite possibly the most emotionally devastating film ever made, I kid you not.
I've heard the effect is similar to watching Schindler's List, but I've not seen the latter, so I can't really comment first-hand.
I cried for the last 10-15 minutes of this film, through the entire credits and for 10-15 minutes afterward.
#4 - Code Geass: Lelouch of the Rebellion: Excellent thrill-ride from start to finish. If you don't like plot-twists being thrown left, right and center, steer clear. If you enjoy a good Xanatos Roulette, you'll probably like this.
#3 - Higurashi no Naku Koro ni: Another great thrill-ride, but in a more down-to-earth setting of 1983 Hinamizawa. There are crowning moments of awesome in just about every arc, and then when the big reveal finally comes in the 2nd last arc of the 2nd series, it's one of those completely unexpected reveals. Great show, but you do have to perservere when you hit the inevitable 'WTF is this shit' moments on the way. This show is like a jigsaw puzzle slowly being pieced together. You can't see the whole picture until it's almost finished.
#2 - The Melancholy of Haruhi Suzumiya: What can I say. This anime is the shit. Eccentric high-schoolers, a bibliophilic alien, a time travelling dojikko and an ESPer that could pass for gay all held together by one of the great snarkers of the animation medium, Kyon. I will say this: Watch it.
*drumroll*
#1 - Fullmetal Alchemist: Now, I know I'm probably going to get flamed for ranking this as #1 when it is, admittedly, plagued by fanboyism and by some standards, somewhat melodrammatic in parts. However, I would argue that its ability to deliver a punchy, witty and humorous story and at the same time deliver some of the greatest impacts I've seen in an anime, such as [span style=\'color:#000000;background:#000000\']Hughes' death and Nina's end[/span], alongside its technical achievement (it was brilliantly animated for its time) ranks it as the greatest anime I have ever seen. It clocks in a bit long at around 50 episodes, but it is one of only two series that was able to keep my attention for a full 50 episodes (Higurashi being the other, which was technically two series).