Ai Love (lifelong). See Everything2.
Akanbe An insulting gesture of pulling down one of your lower eyelids while sticking out your tongue. Anime characters are often seen doing this. See Anime News Network.
Aku Evil. Also the name of Samurai Jack's arch-enemy. See Everything2.
Byouki Sick, illness, disease.
^_^ A basic smiley emoticon commonly used by anime/manga fans. I suppose it probably shows up in actual manga and possibly anime, too. See Kurt's Anime Emoticon Dictionary, Wikipedia, or Everything2.
Chibi Small; shrimpy. Could mean something/someone is cute, particularly in anime, or it could be used as an insult. See Wikipedia or Everything2.
Eigo The English language.
Genki Healthy, happy, hyper, stamina, spirit, and such adjective-nouns. See Everything2.
Gijinka Anthropomorphism, personification. This can refer to simply attributing human characteristics such as speech to animals or inanimate objects, which can be done just in life, or advertising, or whatever, but more specifically might be done in fiction, particularly anime or manga. It can also refer to art (whether official or fan art) in which animals or objects are given at least partially human appearances (or humans can be given at least partially nonhuman appearances). See Wikipedia or TV Tropes.
Giri Obligation, duty.
Ichiban First; the best. See Everything2.
Iro Color. (Also means "lover," or "lust.")
Jisho Dictionary; lexicon; signature; one's own writing.
Joshi Sentence particles. See About.com or Wikipedia.
Kawaii Cute. See Wikipedia or Everything2 or TV Tropes.
Keigo A polite style of speech. This includes honorifics, added to people's names (see people page). See also Wikipedia or Everything2.
Koi Love (passionate, infatuation). Or "carp" (see flora & fauna page).
Kowai Scary, frightening, eerie, dreadful.
Li Chinese land measure. See Wikipedia or Everything2.
Mahou Magic. (See also mahou shoujo on the anime page.)
Matsuri Festival. See Wikipedia. (See also festivals page.)
Nihongo The Japanese language, also called Nippongo. See Wikipedia or Everything2.
Nikkei Short for Nihon Keizai Shimbun, a financial newspaper in Japan, which measures the Nikkei 225. See Wikipedia or Everything2. (Also people who have emigrated from Japan, or people of Japanese descent. See people page.)
Nikkei 225 An index of the leading stocks traded on the Tokyo Stock Exchange. See Wikipedia or Everything2.
Omake Bonus features, extra material. See TV Tropes, Wikipedia or Everything2.
Oricon Style Japanese company which provides music industry information, including charting album sales. See the official website (Japanese only) or Wikipedia.
Pinyin The official romanization system of the traditional Chinese writing system (transliteration from the Chinese alphabet). See Wikipedia or Everything2.
Romaji Japanese term for the Latin alphabet. In English, this usually refers to the romanization of Japanese words (transliterated from Japanese alphabets). See Wikipedia or Everything2.
Suki Love (friendly).
Tabi A journey. (Or socks, see clothes page.)
Takuhai Home delivery. (Also the former name of Tokyopop's Manga Magazine.)
Tareme Drooping eyes. I guess it usually refers to a style of anime or manga in which the characters (usually female) have such eyes (but perhaps might be used to refer to some real people's eyes, as well, I'm not sure). It's a look that connotes such things as sadness or innocence. Very child-like and cute, but is also sometimes associated with hentai (see sexual terms page; discretion advised). See TV Tropes or Everything2.
Terebi is the Japanese approximation of the word "television."
Uzumaki can mean "whirlpool" or "spiral shape." For example, the swirl pattern inside kamaboko or narutomaki (see food page). It's also the last name of the title character in the anime "Naruto" (The name Naruto Uzumaki is a reference to the sliced fishcakes with a spiral pattern). "Uzumaki" is also the name of a J-horror movie involving spirals.
Yuutsu Depression, melancholy. I mention this word here because it's in the Japanese title of the anime "The Melancholy of Haruhi Suzumiya" (Suzumiya Haruhi no Yuutsu). And I suppose it could be in other anime, too. Or whatever.