A priest is a special exalted person with a direct line to God, or the Gods and Goddesses. Ordinary believers don't have that exalted line. So if you want help or favours from any Divinity you ask a priest to contact the divine whatever on your behalf. Some religions have priestesses as well as priests.
Afterwards you mustn't forget to pay the priest or to put money into the collection box.
Roman Catholic priests
—Matthew 19:12 
|“||For there are some eunuchs, which were so born from their mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive it, let him receive it.||”|
Roman Catholic priests take vows of celibacy, and are not allowed to marry. In spite of this, they are supposed to be the primary source of counsel and advice for troubled married couples and families in general. A minority of RC priests abuse children.
Cafeteria Catholics include priests, the "Call to Disobedience" is a movement among priests which started in 2006 in Austria but is spreading to other nations. The movement favours women priests, married priests, allowing Communion to remarried divorcees and non-Catholics among other changes. The traditional Church hierarchy including retired Pope Benedict XVI described them as heretics and Schismatics. By contrast group founder, Rev. Helmut Schüller blames “absolutist monarchy” and resistance to change by The Vatican for a possible rift. Vatican watchers expect the movement to grow. 
Under Pope Francis Australian priest Fr Greg Reynolds was Excommunicated Fr Reynolds, supports women's ordination and gay marriage, Reynolds also publicly celebrated the Eucharist when he did not have official permission to do so.  
The priests are by no means the only Roman Catholics who refuse to follow the Vatican lead, see Disobedient nuns.
- Matthew 19:12
- Pope Rebukes Priests Who Advocate Ordaining Women and Ending CelibacyCall to Disobedience': A Rift in the German-Speaking Catholic ChurchPope Rebukes Priests Who Advocate Ordaining Women and Ending CelibacyOver 300 Austrian priests join ‘Call to Disobedience’
- Pope Francis excommunicates pro-gay marriage priest. He's not the liberal the media wantsPope Francis excommunicates Australian priest
- Pope Francis Excommunicates Priest for Teaching Women
- History of Celibacy in Catholicism: Catholic Priests, Celibacy, Marriage From Atheism.About.com
- History of Celibacy in Catholicism: Catholic Priests, Celibacy, Marriage Page 2 of the above
- Priest Priest from Liberapedia
Adapted from an old RationalWiki article