Gah! How can I limit it to just 5!
1.) Scrapped Princess - One of the first anime I ever watched at TUNAC years ago, and still one of my all time favorites. I rate it on equal terms with FMA as a great anime for jerking around your emotions.
2.) Stellvia - The first Space Opera anime I ever viewed and still among my favorites. I think I have always had a soft spot for school anime, and a school anime in space.... well that's just a win win no matter how you look at it. Nadesico and Vandread are similar and Starship Operators, Planetes, and Crest/Banner of the Stars as well, although the later are much more serious in tone. Shows like Cowboy Bebop and Outlaw Star, I suppose also fall in this category. Love space opera.
3.) Chobits - OK, this is the first anime series I ever rented from Emerald City Comics, and the first I ever purchased. It is the only one I have written a Fanfic for, and the first I got the manga of. Yeah, I think I like this one.
4.) Azumanga Daioh - I don't know if it is my favorite, but it is one of the best comedy, school, slice of life anime ever. I place it next to K-ON!, Ouran Host Club and Toradora as my all time favorite in that genre. I really can't say which I liked the most.
5.) A really hard choice. I want to say Sierei Moribito as the most beautiful animated series I have ever seen, but I also want to mention Full Metal Panic as one of the greatest school and action comedies ever, as well as Inuyasha and Ranma, and Rurouni Kenshin. Mahoromatic also.. GAH! I CAN'T DECIDE!