The role of the clergy, as it is commonly understood, is to intercede between God and the faithful. This means that the worship of the individual needs the stamp of approval of the clergyman before God accepts it. The other side of it is that only the clergyman can interpret God's commands.
An excellent example of the firstissue is how rich and noblemen where excommunicated from the Catholic Church for not obliging the Pope's requests, including material possessions. An excellent example of the second is the interpretation of the Jewish rabbis on the issue of theft, for example. Although the Ten Commandments forbid theft outright, the rabbis interpreted this as only applicable to Jews and not to gentiles.
An interesting showdown between clergy and the faithful was depicted, in a work of fiction,in the novel-turned-to-movie "The Name of the Rose" by Umberto Eco. The reader would probably remember the debate that took place in the abbey about the poverty of Christ.
The story tells that the representatives of the papal throne argued against this concept, and were willing to burn people at the stake for their belief in the poverty of Christ. The corrupt clergymen would rather burn people alive than admit that Christ led a life of austerity, because if they do they will be asked a very fundamental question: why are you not behaving like Christ when you are supposed to be holy men? Granted, not all that was narrated in Eco's masterpiece was correct, but I gather that a lot was.
Such a showdown is alien to Islam, because the concept of Islamic worship is unique. The Prophet (peace be upon him) said to his companions (I will paraphrase because knowledge of Arabic idioms is necessary if I just transliterate): "The act of copulation with one's wife is worship." The companions were astonished by this and said: "How come? We are fulfilling our desires. How could this be worship". He replied by saying: "If one copulates with a woman who is not his wife, would this person be sinning?". They all agreed. He said then: "Thus with one's wife, it is worship".
In Islam, every little act of life, if carried out in good faith and with good intentions, is considered worship. Praying, fasting, giving away charities are worship, but sleeping with the wife, buying food for the house, cooking a meal, driving the children to school, playing with one's children are also worship. Clergymen are useless in such a system.
After making sure that there is no confusion about what is considered worship for a Muslim, the next phase is to clarify the issue of religious authority.
During the life of the Prophet (peace be upon him), he was the absolute religious authority, for if one believed that he is was prophet, one must have accepted all of his religious teachings because he was commanded by God.
Accepting did not mean blind faith without understanding. Many a times the companions questioned, debated, and flat out refused some of the commands given to them by the Prophets (peace be upon him), but finally accepted when they comprehended the true nature of the commands and their rationale.
However, after the death of the Prophet (peace be upon him), religious authority reverted back to the Qur'an and to his -the Prophet- teachings, which carried the general guidelines. God orders the believers in the Qur'an to: "Ask the scholars if you do not know". And once the point in question is clarified, the final authority is oneself alone.
The Prophet (peace be upon him) says (I am paraphrasing): "Make the decision for yourself even if the scholars tell you this or that". This means that one will be responsible for one's actions before God and cannot blame someone else for what he/she does, as long as he/she commands sufficient knowledge and common sense. To render this fair though, God tells us in the Qur'an that He pardons forgetfulness, mistakes and what is beyond our faculties and capabilities.
The bottom line on this second issue is this: No one will answer on your behalf before God, so you better make sure what the scholars tell you is the truth, to the best of your knowledge and ability. Again, the clergy system is useless here.
Lastly, there is no one infallible in Islam. This is a very focal point, since if no one is infallible then anyone is liable to making mistakes. And since this is the case, then no one has absolute monopoly on the truth. Such system, once again, has no place for clergy.