Simple enough question, ne? But you're only allowed
one answer ... I for one could list a dozen or so anime that I really adore. So, let's just keep it to the one anime that you love most dearly -- the one that you would choose if you could only watch one anime again (and it can definitely be either series, OAV, or movie ^_^).
As for me? My unquestionable favorite is Escaflowne (though a few others have come very close!). It was the anime that really introduced me to, well,
anime. The wonderful characters, epic plot, and even those ever-present shiny hair halos and long noses have all made sure that I will never forget it. I feel happy whenever a song from the excellent (Yoko Kanno!! Hajime Mizoguchi!! Maaya Sakamoto!!) soundtrack comes up on my iTunes. I have good memories associated with this show, and I can't imagine I will ever tire of watching it (I own both the dubbed VHS and the individual DVDs, as well as the special edition of the movie

).
*The pretty bishounen don't hurt either ^_~*
Mine would have to be a toss up between Rurouni Kenshin or Slam Dunk. I can watch these series over and over and I don't think I will get tired of it quick. I just finished rewatching Slam Dunk series like a couple of months ago. ^_^
If I can't use a coin for my selection between this two.. I guess I'll pick Rurouni Kenshin.
Ooo, this is a hard one; but as much as I love other series I'm gonna have to say Nadesico, very closely behind though is Chrono Crusade. Then I'm only saying Nadesico for the fact it is about the only anime that had me loose track of time watching it. I stared it in teh day watched until it was night and didn't even notice.
I gotta go with an old classic here and say Doraemon. Growing up in Hong Kong, every child knows Doraemon and its (Chinese) theme song by heart. I remember always rushing to the nearest newsstand whenever a new tankobon comes out and reading it a million times afterwards. Doraemon wasn't just an anime in HK, it was part of our generation's culture. It taught us many life lessons, and whenever I want to be a kid again, I can just open up a copy of Doraemon.
To a lesser extent, Fruits Basket and The Melancholy of Suzumiya Haruhi would be my runners-up. Furuba shows us what a "perfect person" (Tooru) would be like, and it also managed to bring tears to my eyes. As for Haruhi, it's definitely the most unique way to present a story. By "messing" with the story's chronology, it really challenges the viewer's perception of conventional story-reading/viewing. Both were worthy choices but alas, they do not have the immense influence as Doraemon.
My god this is so hard for me....As for now I have to say Saiunkoku Monogatari. Engaging plot, unique characters, beautiful setting, decent animation, top-notch soundtrack....That's all I need

. I'm not going to mention what follows behind but my friends all think that Busou Renkin is my favorite...and it's not

. So don't get that impression no matter how many times I mention it

.
Escaflowne was what first introduced me to anime. But, it isn't my favorite. I have a three-way tie between My-Hime, Chrno Crusade, and Fruits Basket (with His and Hers Circumstances as well as Trinity Blood coming in at honorable mention)...
However, if I must pick one, just one .... I will go with the first anime I've ever seen and it was Miyazaki's Howl's Moving Castle followed closely by Princess Mononoke.
I never knew animation combined with beautiful music and a powerful storyline could make me cry so much.
Favorite manga: Rurouni Kenshin
Favorite anime: Wolf's Rain
Favorite manga: Rurouni Kenshin
Good taste! ^_^
As of right now it is Laputa:Castle in the sky
I would say Rurouni Kenshin hands down