Many people will throw around compliments like "The Best" rather easily, and change their minds like the wind. I dislike using that level of description, because usually there's several things competing for that position.
Not, however, in the case of anime series. No series I've ever watched -- and I've watched a lot of them, from Mobile Suit Gundam to Harlock to Metal Fighter Miku and Space Adventurer Cobra -- comes close to matching Escaflowne.
Visually, Escaflowne is stunning. Most series animation is clearly inferior to that found in anime movies, but in the case of Escaflowne it's hard to recognize that this is, in fact, a series. The backgrounds, the main characters, the action, all are done with a warm, lush attention to effect that never fails.
The music is one of the finest anime soundtracks ever made. Composed by Yoko Kanno (Macross Plus, Cowboy Bebop), it captures a spirit of mysticism and high adventure which is perfect for this series. I often leave this disc running in the background because it's so much fun to listen to.
The story... how can I do it justice? The best way to put it is this: for the past several years I have done a monthly anime night at our local Borders, and Escaflowne is the ONLY anime to consistently pull in people of all walks of life. I've seen it enthrall Dragonball Z fanboys, Sailor Moon addicts, 65-year-old grandmothers, 7 year old little brothers, casual Yuppie passers-by, and cynical goth poseurs. It has magic and war, politics and romance, intrigue and action, swords and giant mecha suits, and somehow all of it works to form a dazzling coherent whole that is unmatched in all the history of animated television.
Watch Escaflowne. You will never regret it.