千と千尋の神隠し (Spirited Away) is a fantastic anime. I find it interested that almost all of the people posting in this thread have similar opinions of Miyazaki Hayao's (and Takahata, but Miyazaki has always (I think) been involved in Takahata's work) animations. My personal favourite of Ghibli's is 耳をすませば (Whispers of the Heart). But I have loved all of Studio Ghibli's releases, including some of Miyazaki and Takahata's pre-Ghibli works (e.g.: パンダコパンダ) 'Though you're all probably familiar enough, a good reference for Ghibli works is:
For the record, I like almost all types of anime (some hentai is a little much for me...). Recently, I've watched "Excel Saga" - a great anime that makes fun of other anime. I've been watching Rurouni Kenshin and Noir also. They are very good.
I cannot pick a favourite of all time, because each genre is different and I like some better than others depending on my mood.
I'll try, but usually most recent is most remembered and thus most liked (I tend to fall in love with characters easily):
Television series: Love Hina (ラブひな) but Angelic Layer is a close second (気道天使アンジェリクレイヤー) and I've been wanting to see Akazukin Chacha (赤頭巾 チャチャ) because I've heard so many great things (yeah, I'm the kind of sicko who likes Mahou shoujo)
OVA Series: FLCL (フリクリ)
Movie: Anything from Ghibli, but specifically Whispers of the Heart (耳をすませば)
But realistically, I like everything. I am annoyed when they have stupid, depressing endings. (e.g.: grave of the fireflies, berserk, Trigun, cowboy bebop)