I cannot narrow down my top 5, so here are 5 more..
6. Saikano - This show drew me in and ripped my emotions to pieces. I watched this in one sitting and will never forget it.
7. Berserk - This anime is awesome. Beyond it's stylized appearance, the show has an orignal and twisting plot and great character development. My only complaint is that the last few episodes are horrid. I cannot stress how badly this series ends. It's 10 times worse than any average anime ending.
8. Onegai Teacher - This one is a little more touchy-feely that I usually watch, but it has good humor and takes your emotions on a roller coaster ride. Plus this one has a happy ending.
9. Blood the Last Vampire - The art and story (while short) is very top notch. There is also a series based on this movie called Blood+, which is good as well.
10. Great Teacher Onizuka - Although this one falls on the perverted side, there is a genuine humanity to the main character. It's an outrageous comedy that sheds a positive light on not so positive issues. I remember that this anime helped me out when I was feeling down.