First, the obligatory message: The Bible is clear that God designed people to have sex only within the context of marriage. Sex outside of marriage is wrong, whether it is for pleasure or any other purpose (1 Corinthians 6:18).
Is sex intended only for procreation or can married couples have sex just for pleasure?
Nowhere does the Bible prohibit sex for pleasure. In fact, the Song of Solomon roundly approves of sex for pleasure. The origin of the church's stance against sex for pleasure is a bit convoluted and not well documented until the sixteenth century. The Council of Trent (1546) declared that amor concupiscentiae, or sensual longing (i.e.: lust), was not sin in and of itself but did have the potential to lead to sin. Eventually, the Catholic Church formally decided that sex for the sole purpose of pleasure was not appropriate. Not necessarily because of the birth control issue, although they insist that every sexual encounter must be open to the possibility of pregnancy, but because the sex act is a worshipful expression of the love, self-sacrifice, and union of the marriage relationship.
This is deeper and richer than sex for pleasure, and it is certainly biblical to appreciate sex as a physical manifestation of God's statement that "they [the husband and wife] shall become one flesh" (Genesis 2:24). This point of view is also supported by 1 Corinthians 7:3-5. Individuals who seek sex merely for physical pleasure—even within a marriage—are not exemplifying the spirit of mutual submission God intended. Sex should be a part of and a result of a loving marriage relationship, not merely a physical release.
But when the topic of "sex for pleasure" is broached in modern times, it is usually within the context of birth control, and here the Bible has little to say. As has been explained in other articles, the Bible is not against the judicious use of birth control. In addition, nowhere does the Bible state that a physically infertile couple must not have sex. In that way, it is perfectly allowable for a couple to have sex for reasons other than the attempt to have a child.
Does God expect everyone to have children?
Does the Bible say anything about permanent forms of birth control?
How often should married couples have sex?
What is/isn't a Christian married couple allowed to do, sexually?
In marriage how do the two become one flesh?
Truth about Marriage