As others have noted, in international correspondence play, conducted under the auspices of ICCF, computers are allowed. Correspondence chess has been an interesting battleground for this debate because it has been stated above, the primary strength of the computer is brute force calculation and speed. When Botvinnik was first attempting to design a chess computer program, he was hoping to develop a true AI. Instead, modern computers win because they simply can calculate many more possibilities and pathways than a human could in a given amount of time. A human might miss the best continuation simply because he or she doesn't have adequate time to analyze it. Correspondence chess solves this issue because the human has considerably more time to analyze, whereas the computer doesn't really benefit from being able to examine the same position for several days. Interestingly, I should point out that there is quite a lot of evidence supporting the argument that humans contribute greatly to overall performance.
First, back in 2005, Arno Nickel, one of the strongest correspondence chess players in the world, played a four-game match with Hydra, which at the time was arguably the strongest chess-playing supercomputer in the world. Nickel was allowed to use a PC and chess software that he had bought off the shelf, similar to what he would use in an ICCF tournament. In a straight-up match between Hydra and the basic PC software, Hydra would have won every game. In the actual match, the match ended early because Nickel crushed Hydra 2.5-0.5 (two wins and one draw for Nickel). In other words, the combination of man and weak machine was too much for the best super-computer on the planet.
Second, there is a variant of chess called Centaur chess. Centaur chess involves a human-computer team. Humans make the move, taking into account analysis by the computer. At first glance, one would expect that this is simply a matter of who has the best computer software (and many of the players have developed their own chess programs). However, Centaur tournaments allow participation not just by human-computer teams, but by stand-alone computers without human assistance, and usually about half the participants are such stand-alone computers. To my knowledge, every one of these tournaments has been won by a centaur, i.e. the human-computer teams always beat the computers.
So, while it is true that the average human player would have little chance against an equal human playing with a computer, it is also true that computers have little chance playing against an equal computer playing with a human. All of which suggests that humans still contribute to the game, even when computers are involved.