Can a Christian ever get divorced?

Yes, a Christian may divorce for sexual sins, for desertion, and for other marital offences of a similar nature. Jesus specifically allowed divorce for fornication, or sexual sins (Matt 5:31-32; 19:3-9). Paul allowed divorce for desertion (I Cor 7:12-15,27). Jesus also taught the principles of mercy (Matt 12:1-8) and intent (Mark 2:23-28), which allow divorce for other serious faults.

See Also

Sermon and outline about adultery and divorce: Sermon on the Mount.
Sermon outline on I Corinthians 7, including verses 10-16: I Corinthians 7.
Proverb commentary about just judgment and mercy: Proverbs 21:3.