Legally licensed sites are good for watching anime while keeping your computer safe and you out of trouble.
Lavender recommended Crunchyroll, which I've used A LOT! Crunchyroll has a lot of free anime. The subscription service is great for staying ahead of the game. They also have dramas, which I recommend giving a try if you ever find the time (starting with Goong and My Left Eye Sees Ghosts). They also recently added a Manga section for Manga and Premium subscribers
Funimation-
http://www.funimation.com/Anime Network- Color marks will indicate free and non-free stuff
AnimeNewsNetwork actually has a few anime, now that I think about it...
Youtube has some free anime from the licencors
Viz- arguably not the best with subs
There are a few more. I'll update as I find them or feel free to post more legal streaming links.
NiciNico-
http://www.nicovideo.jp/video_top/animeAnimeSols-
http://www.animesols.com/Crackle-
http://www.crackle.com/c/animeDaisuki-
https://www.daisuki.net/ Quality in question
Viki-
http://www.viki.com/ Still looking into this one...