Not that I am at that level. I just watched Spirited Away (千と千尋の神隠し) in Japanese to test how much I know now that I've finished the Absolute Beginners series, and I understood about one word in twenty.
I've watched a handful of anime series these past two weeks without subtitles. Sword Art Online, Death Note, and Fullmetal Alchemist: Brotherhood, to name a few. I'm on the same page as you; I pick up one one out of every twenty or so spoken words, which I think is great progress.
I've found that watching and listening to anime without subtitles really helps to reinforce my understanding of the language, the context, and the speed in which words are spoken. Though, it should be noted that one shouldn't rely solely upon anime for improvement. Give live action Japanese films and newscasts a try, too.
Sheegoth are large predatory creatures native to the frigid Phendrana Drifts region of Tallon IV from Metroid Prime.
I'm starting to learn Japanese again after a 6 month hiatus and I'm watching Kaseifu no Mita (I'm Mita, Your Housekeeper) on Crunchyroll. I'm watching each episode raw first and then with subs (so I'm doing things the other way around to jayr1063). Not sure whether I'll keep it up until the end of the series though, I might just do half and then watch the rest subtitled.
These days it's common for anime to be done with "soft subtitles", so when you download anime from any of the numerous fansub companies out there, if you use a media player like VLC, you can disable the subtitles. If all else fails, get dual audio because then you can switch the language to Japanese and disable the subtitles.
I've been watching Naruto without any subtitles. I understand enough grammar and vocab to vaguely follow the story, and when I keep hearing a word/phrase/etc. over and over again, I look it up on Denshi Jisho or something. It's really fun, and I find myself disagreeing with subtitles sometimes!