I would estimate the answer to this question as somewhere between 0.35 and 0.58 in our dependency upon them...
a chess engine are merely stored up possibilities of several ways the game of chess can go, there pros and cons to each way, and ways to nullify the strategic and tactical advantages and disadvantages that arise in any direction, it is for the human player to choose the direction that he wishes to proceed, use the engine to refine your practical strategy that suits you, you may pick up some stuff that you over looked, but end of the day when you at the board analyse the board choose a move in which you have a proper follow through by logic of tactical exploitation or reasoning of strategic evaluation, place faith in the capability of the human mind it is not obsolete, don't sit at the chess board asking what did the computer do, look at the board analyse the board, use the logic and reasoning of the human mind, it is still the most practical way to play chess
I believe that computers tell us how to play and make the most safest and the most perfect of moves and basically that's how "PERFECT" chess looks like! And I don't blame them... they work on algorithms written by humans. But like any algorithm ever written; it's heartless! For me I feel that positional players like Capablanca, Karpov etc would completely fall in love with the way an engine plays but the engine won't be able to impress Tal or Shirov much!
But I believe that evolution is taking place... I recently saw a game between Houdini and Rybka and felt delighted by the way Houdini played. It was still quite positional but in a Tal fashion (via. sacrificing pawns early in the opening).
SHORT ANSWER: YES! Most of us rely too much on engine analysis and that has seriously costed us in the department of innovation!