There are many issues where religion and politics overlap. e.g. Abortion, Homosexuality, Environment, Evolution, Celebration of religious holidays in public places, The 10 Commandments in public buildings, prayer in school, ....

There was a lot of talk about the "Religious RIght" having a big effect on the 2004 presidential election.
There is certainly a big overlap with conservative Christians and the Republican Party, but the question of where the boundaries are between religion and politics would take up volumes.

These issues also cause controversy within churches. In 2005-2006 there were heated discussions over homosexuals and women in the clergy in the Episcopal and Southern Baptist churches as well as others.

A New York Times Article on July 30, 2006 titled "Disowning Conservative Politics, Evangelical Pastor in Minnesota Rattles His Flock", discusses Rev. Gregory A. Boyd who preached six sermons called "The Cross and the Sword" in which he said the church should steer clear of politics, give up moralizing on sexual issues, stop claiming the United States as a "Christian nation" and stop glorifying American military campaigns. This was after multiple attempts to get him to preach on these topics.

Some Topics I've started to document:
Creation vs Evolution
Religion and the Environment

Homosexuality - Gay Marriage

Jesus didn't have anything to say about homosexuality in particular. Some people say that his reference to sexual immorality (the King James translation uses fornication here) in Mark 7:20 refers to homosexuality.

Paul says in 1 Corinthians 6:9 that homosexuality will keep you from entering the kingdom of God.

Marriage:
I couldn't find anything in the bible specifically about marriage between a man and woman. There are several references to husbands and wives.
In Matthew 19, Jesus talking about divorce says "He which made them at the beginning made them male and female, And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh?"

See Gay Marriage (Homosexuality)

Environment:
Forty-five senators and 186 representatives in 2003 earned 80- to 100-percent approval ratings from the nation's three most influential Christian right advocacy groups -- the Christian Coalition, Eagle Forum, and Family Research Council. Many of those same lawmakers also got flunking grades - less than 10 percent, on average - from the League of Conservation Voters last year.
This is more difficult to explain based on the bible. Grist.org explains it as follows:
"Many Christian fundamentalists feel that concern for the future of our planet is irrelevant, because it has no future. They believe we are living in the End Time, when the son of God will return."

Links:
What does the Bible say about marriage?
Biblical marriage: a bad source for debate
Fundamentalism
Books:
God's Politics, Jim Wallis
Partly Right: Learning from the Critics of Christianity, by Tony Campolo
Is Jesus a Republican or a Democrat?: And 14 Other Polarizing Issues by Tony Campolo