i watch most of anime online now. but i'm only going to recommend legal, commercial ways (you have to either watch commercials and/or pay a monthly fee).
Crunchyroll - has the most simulcasts (subs that come out the at about the same time that the episode originally airs in japan). it has a huge library of older anime too. they're almost all subtitled though. you can watch it for free with commercials, or subscribe to it (which i do). you can also watch Crunchyroll on devices like a PS3, XBox360, and several smart phones.
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Funimation - the official site for the anime dvd dubbing company. when they get a new license to a series, they often time release the subtitled version of the series for free with commercials (sometime this is simulcasted). they also often let you watch the first several episodes of many of their dvd series dubbed. if you subscribe to them, a large quantity of their dvd library becomes available to watch (i don't subscribe).
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Hulu - they have a large library of anime dubs (subs if a dub isn't availabe). you can watch many of their shows for free with commercials in it. if you subscribe to Hulu Plus, there's more episodes that you can watch, plus you can watch it on devices like a PS3.
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Viz Anime - the dvd dubbing company's official site. you can watch many of their shows on their site (powered by Hulu).
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YouTube - they have a ton of anime series often dubbed that you can watch with commercials. i'm not sure if they can be watched on devices like a PS3 or smart phone.
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Nico Nico Douga - a Japanese youtube-like company. they have an English version and host several simulcasts. i'm not sure how to get to the current page that has full anime episodes or simulcasts though (it's tought to navigate)
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Netflix - only available with a subscription fee, but lots of families subscribe to Netflix, so there's a good chance you might be able to watch it. they have a good assortment of anime dub series. you can also watch it on a PS3, XBox360, Wii, smartphone etc.
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Anime Network - you have to subscribe to watch most episodes, but they have a large assortment of dubs and subs and a couple simulcasts. the first episode of most series is available without a subscription.
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