Appleseed is an Anime based off the manga by the same name. The creator is Masamune Shirow, the same artist/creator of Ghost in the Shell. I like both Ghost in the Shell and Appleseed equally albeit for different reasons.
Whereas GITS is more scientifically philosophical, Appleseed as a series is more fun and entertainting in the traditional sense. The 2004 movie (image above) is a combination of two story arcs from the original series. It remains a philosophical theme of "what is the definition of 'humanity' and of being human?" The moral debate in Appleseed focuses on humanity's corruption and prejudice against anything not human. Shirow takes this farther in GITS when he brings in the debate of cybernetics and the consciousness of anything living. GITS asks the question of what is the soul?
These series are both great. Appleseed is more light hearted with more humor, and GITS is more of a realistic and philosophical tone. The Appleseed movie (2004) however utilizes a tone much more in the vein of GITS. However, this doesn't subract from the story, nor the wonderful cast of characters. The 3-D animation is gloriously well executed, stuningly beautiful, and considering they did Appleseed on about 1/3 of the cost (aprox. $10 million) which PIXAR typically funds its films with ($150 million)... I must say I am doubly amazed.
I recomend any of the classic Appleseed anime or comic series, and for me personally, Deunan and Briareos are two of the coolest characters ever created. Major Kusinagi is a close second.
The animated television series Ghost in the Shell: Stand Alone Complex is probably the best Anime I've ever seen. I place it above Cowboy Bebop and Escaflowne as far as quality of story telling and animation goes. I picked up GITS: Stand Alone Complex when I was in Japan, and was truely awe struck. Oddly enough the latter three seires music is composed by Yoko Kano. She's wonderful! I also loved her score to Shimotsuma Monogatari.