"Style? I have no style." – Anatoly Karpov

Karpov in a Gibralta interview indicated he is like Petrosian but playing for win!

Petrosian influenced heavily by Nimzovich

"Let us say that a game may be continued in two ways: one of them is a beautiful tactical blow that gives rise to variations that don't yield to precise calculations; the other is clear positional pressure that leads to an endgame with microscopic chances of victory. I would choose the latter without thinking twice. If the opponent offers keen play I don't object; but in such cases I get less satisfaction, even if I win, than from a game conducted according to all the rules of strategy with its ruthless logic." – Anatoly Karpov

Note that this may also be very useful in reverse :) - in choosing potentially bad continuations, choosing one that is bad but you know how bad it is (a "clearer picture" of how bad it is), is often better than choosing something which you are not sure how bad it is because for example of a piece sacrifice which opens your king and you are not sure if you are being mated.  The key thing is having clarity about continuations whether they are good or bad :) Chess for Karpov is a game of control, and not leaving things to luck and chance.  Another perspective here is not to have any mystery "black boxes" which you don't really know what is inside. Keeping continuations clear means fewer mystery "black boxes".

"I simply developed that universal style which dominated with the arrival of Spassky and then Fischer. But all the same we were different chess players, of course. Both Spassky and Fischer were brilliant at developing and sensing the initiative. In that regard I was, perhaps, a little inferior, but on the other hand I stood out by having excellent technique for converting an advantage, positional sense and an ability to maneuver positionally – in that area I was clearly superior to Spassky, and Fischer, and perhaps everyone, except Petrosian." - Anatoly Karpov

"At first I found some of his moves not altogether understandable, and only after careful analysis did I discover their hidden strength. – Ljubomir Ljubojevic (on Karpov)"

"When observing Karpov's play or playing against him, one cannot help thinking that all his pieces are linked by invisible threads. This net moves forward unhurriedly, gradually covering the enemy squares, but, amazingly, not relinquishing its own. – Alexander Roshal

"When having an edge, Karpov often marked time and still gained the advantage! I don't know anyone else who could do that, it's incredible. I was always impressed and delighted by this skill. When it looked like it was high time to start a decisive attack, Karpov played a3, h3, and his opponent's position collapsed. - Vladimir Kramnik"

"Many of Karpov's intentions become understandable to his opponents only when salvation is no longer possible. – Mikhail Tal"

"Known as a negative player, Karpov sets up deep traps and creates moves that seem to allow his opponent possibilities - but that really don't. He takes no chances, and he gives his opponents nothing. He's a trench-warfare fighter who keeps the game moving just an inch at a time. – Bruce Pandolfini

"If I see an aggressive option that's the best, I will go for it", and that "if there are several approximately equal opportunities, I will go for the simplification".