Jesus never mentioned homosexuality, but He did condemn all forms of sexual immorality:
What comes out of you is what defiles you. For from within, out of your hearts, come evil thoughts, sexual immorality, theft, murder, adultery, greed, malice, deceit, lewdness, envy, slander, arrogance and folly. All these evils come from inside and defile you. (TNIV, Mark 7:20-23)
The apostle Paul, in one of his letters to the Corinthians, wrote the verses most often quoted on this subject:
Do you not know that the wicked will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor male prostitutes nor homosexual offenders nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God. And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God. (NIV, 1st Corinthians 6:9-11)
This verse has been translated in as many different ways as there are different versions of the Bible, so we have to look at the original Greek to see what Paul was really saying. According to Thayer's Greek Lexicon, the word translated here as "male prostitute" is the Greek word malakos which literally means "soft to the touch." However, it was used metaphorically in a negative way to refer to a catamite (a boy kept for sexual relations with a man) or to a male prostitute in general. The word translated here as "homosexual offender" is the Greek word arsenokoites which means a sodomite, a person who engages in any kind of unnatural sex, but especially homosexual intercourse. Some believe this use of arsenokoites referred specifically to the men who kept catamites, but that is not certain.
There are two other New Testament mentions of homosexual acts, in Romans 1:25-27 and 1 Timothy 1:8-10. In this passage from Romans, again in the context of idolatry, Paul mentions women who "exchanged natural relations for unnatural ones," which might apply to lesbian acts: