I would love to learn Japanese, specially due to my liking for anime. Are there any sites where I can devote 1-2 hours a week to develop basic Japanese speaking skills?
I recommend starting with Memrise. You can quickly build a strong vocabulary by working flashcards sets anytime you have a spare moment, and it has an app for mobile use. The more words you recognize, the easier it is to understand what is being said or written. Grammar and building sentences should come later, and is best done within an active community where you can get interactive feedback.
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.
Well, I'm just a beginner and only interested in speaking Japanese... Haven't thought about writing though.
Duolingo is fantastic. Unfortunately they don't have Japanese yet but they add new languages regularly so I wouldn't be surprised to see it added soon.
I would never do this, of course, as I'm a prime rib beef, monster truck driving, red blooded American citizen, but I've heard stories about people who've gone to strange lands run by peg-leg pirates sailing ships of booty, and brothels run by kick-ass kats, with torrential thunderstorms cackling across the magnetic sky. These people would scribble on a piece of paper the words "Rosetta Stone", hold hand out while amidst a teeming crowd, an unknown hand would whisk the note away --and, miraculously five days later, a copy of the Rosetta Stone written in the specific language in question would arrive on the peoples' doorsteps, brought by winged doves with olive branches in their beaks. I think this happened in communist Russia.
if you have a library card, you can gain free access to the Mango language app. Felt as if I were making good progress for the time I applied myself.