Dennou Coil (TV series)
Escaflowne (TV series & movie)
Evangelion (TV series & movies)
Ghost in The Shell: Stand Alone Complex (TV series)
Gundam Seed (TV series)
Kimagure Orange Road (TV series)
Robotech series (particularly the Macross and Mospeada segments)
Rurouni Kenshin (TV series & OVAs)
Whisper Of The Heart (movie)
Of course I could also includes all other Miyazaki movies (beside Nausicaa I particularly like Laputa, Totoro, Porco Rosso, Mononoke Princess) and series (particularly Future Boy Conan, Red-haired Ann), Akira (movie), Beck (TV series), Blood+ (TV series), Bubblegum Crisis (OVA series), Cowboy Bebop (TV series), Dot Hack//Sign (TV series), Fantastic Children (TV series), Giant Robo (OVA), Grave of the Fireflies (movie), GTO (TV series), Gunbuster (OVA series), the Gundam OVAs (0080, 0083, 8th MS Team), Hataraki-man (TV series), Initial D (TV series), Irresponsible Captain Tylor (TV Series), Kacho Ohji (aka Black Heaven, TV Series), Kare Kano (TV series), Megazone 23 Part II (OVA), Moyashimon (TV series), Nadia: Secret of Blue Water (TV series), Nana (TV series), Night Head Genesis (TV series), Nodame Cantabile (TV series), Noein (TV series), Paradise Kiss (TV series), Patlabor (series & movies), Rahxephon (TV series), Record Of Lodoss Wars (OVA series), Seirei no Moribito (TV series), Tide Line Blue (TV series), Twelve Kingdom (TV series), Wings of Honneamise (movie), Witch Hunter Robin (TV series) and so many more. But it gives you an idea.
Blade of the Immortal (L'Habitant de L'infini)
Ghost In The Shell
Please Save My Earth
Rose of Versailles (Lady Oscar)
I could also includes all the other works of Osamu Tezuka (beside Buddha I particularly like Astroboy, Dororo, Kirihito, L'arbre au soleil) and of Jiro Taniguchi (L'homme qui marche, Au temps de Botchan, etc.), but also Akira, Area 88, Beck, Cat's Eye, City Hunter, Fushigi Yuugi, GTO, Ikkyu, Rouruni Kenshin, What's Michael, Yakitate Ja-pan, etc. Most of those title are available both in English and French, and most of them I would recommend to a beginner (save maybe Ghost In The Shell which is too cyberpunk hardcore and difficult to follow). Strangely, I have much more trouble listing my favourite manga than anime (probably because I've seen more anime than I've read manga).
There you have it. Now, stop asking me which are my favourites!
For my other favourites (blogs, books/comics, interest, movies, music) check my profile.