They played the Berlin defense and Ruy Lopez. Well the question is more like: why Anand insisted to play Ruy Lopez again and again. wouldn't be better if he had tried najdorf and nimzo indian earlier? I felt like Anand is giving Carlen the world championship as a thanksgiving gift! Why would a GM in a world championship be so stubborn. What was he hoping for and what was his plan by insisting to play the same opening?
One of Anand's strengths relative to Carlsen is better opening knowledge, and Anand also had the better analysis team. (UPDATE: According to Carlsen in a recent interview, his team of seconds during the Chennai match consisted of Hammer, Fressinet and Eljanov.) To repeat openings was a natural match strategy for him, trying to turn the match into an opening discussion.
By varying openings, especially with white, Carlsen cleverly avoided most of Anand's preparation. The only set-up that was repeated was
d3 against the Berlin (played in two white games by Anand), but Anand couldn't find any weakness there. Anand has played
1.e4 most of his career, and it's understandable that he tried to catch Carlsen there. The one game Anand played
1.d4 he lost, although probably from a strong position.
Yes, Anand should have taken more chances, but even with hindsight it is difficult to devise a match strategy for him leading to success.
Before every important match, opponents are very carefully preparing their repertoire of openings/defenses. This not only include deeply training of known lines, but also their own analysis how to invent new continuation, that could suprise the opponent. Because when that happens it often leads to easy win.
So even before the first move of first game they both know how they will play and even to what exactly continuation each one will want to proceed.
In my view, in terms of opening preparation, the Anand team failed to obtain middle game positions that suited Anand's style. In general, I think that Anand should have aimed for long middlegames with most pieces intact. While Carlsen should have aimed for long endgames with most pieces exchanged off the board. From this point of view, Carlsen got his types of positions, while Anand failed to get his. This can partially be explained by the chosen opening systems. Additionally, I think that Anand should not have willingly exchanged queens in a single game.
He couldn't play Najdorf, as Carlsen would have played 3.Bb5+ (as he did in the last match game). He also couldn't know that Carlsen would go for the Nimzo-Indian against 1.d4, it could as well have been a dry Queen's Gambit Declined.
I think Anand's team had things prepared in various lines of the Berlin Defence, but not against the exact variations that Carlsen had chosen.