League of Legends - http://eune.leagueoflegends.com/ League of Legends - homepage. Its divided by game server - North America, EU West, EU Nordic & East, Brazil, Turkey. This is link to the EU east website where I play.
Mobafire - http://www.mobafire.com/ Great databese of hero guides. You can also find all types of lore and game data there. They also have their own MobafireTV and list of League of Legends streams.
Solo Mid - http://www.solomid.net/ Another great guide database for League of Legends. You can also find there a lot of video streams and other videos.
Favorite guides
Who is your jungler and what does he do? na Mobafire Great guide with summary of all junglers with their comparison and rating. How to play with and against them. Guide also contains a lot of youtube videos with gameplay.
Finding your Fit: Champion selection na Mobafire Great guide for starting players about what heroes to pick. In the second part there is a text about "Dealing with how you feel", from which can greatly benefit even expirienced players.
Rune tips na Mobafire Great guide for newbie players about runes - what ruens are good for what and why to buy them or not.