I want to know if there is any web site that maintains the recording of the famous chess tournaments. I am not looking for the video recordings, but the recording of the moves. For eg. I am currently looking for all the recent matches held between Carlsen and Anand in November, 2014.
I would recommend chessgames.com.
For example, if you want to find out more about the Zurich 1959 tournament, just go to the mentioned site, find a link to Collections and search for Zurich 1959. You should be able to find this link, with the list of all games played there, sorted according to rounds.
To find all games between Carlsen and Anand in 2014, just use the search bar on the homepage of chessgames.com. To find the WCh match in 2014, follow the above procedure and it should lead you to this link.
This Week In Chess is probably the best place to go for those. New game files are posted weekly. Though in the case of Carlsen-Anand 2014, it's probably available from dozens of places, including the official website of the match itself: http://www.sochi2014.fide.com/results/
I recommend you this, it is one of the oldest and best chess database, containing most of all the recognized rated games. Also, there are lot of features in here, for example: You can make your moves or place a position on the board you wish and search for the same kind of position played by any player and then also go through the whole game.
Also there is computer analysis to the downright of the screen to check what the computer evaluates after each move.
Hope this helps. :)