For learning kana and kanji, the Japanese writing systems, I'd highly recommend Read the Kanji. It's great for learning to read words, but terrible for learning to recognise the kanji individually, or remembering how to write them. I think that it's free for learning kana still, which are the two basic "alphabets".
I've heard good things about textfugu, but haven't tried it yet. The first set of lessons is free though, so you also have nothing to lose there if you're just beginning.
Finally, you should check out the Japanese Learning Stack Exchange site, which is a great resource in and of itself, and anki, which isn't a web app, but a flash card program. There are lots of decks for anki on ankiweb, and it's a fantastic tool for memorisation in general.