The usual belief is that there are only three motives why people indulge in sexual activities
To make baby (procreation)
To feel good (pleasure)
To express love (passion)
The belief is now changing as people are citing more and more reasons for indulging in sexual activities than in former times.Some of the most frequently cited reasons are
Relieving depression
Reducing sex drive
Boosting of power
Improving social status
Feeling loved by partner
Showing love to partner
Fostering jealousy
Taking revenge
Making money
Part of duty
Pressure from partner
Making baby
Getting pleasure
Out of curiosity
Seeking novelty

Is there any difference between male and female?
Yes, men usually seek sex because they like how it feels.  They concentrate more on bodily pleasure. Women on the other hand are generally more interested in the relationship enhancement although they also feel pleasure out of this act. Relationship becomes more important for men as they grow older and older. On the other hand women also can focus on pleasure after initiating, developing, and maintaining a long term relationship.
It has been seen in recent years that the male and female stereotypical sexual behaviors don’t stand out but there is a convergence. More women now prefer to indulge in sexual activities for physical pleasure only, whereas more men are looking for emotional closeness and long term relationship.

The basic reason
To figure out the motivating factors why people seek sex is not a simple task. Sexual behaviors have different social, cultural and religious meanings. There are conventional appropriate reasons for having or avoiding sex. These have different implications too. 

What may be the motivating factors to seek sex, at the most basic level, there is one and only one reason. We are programmed to do so just like we are programmed to eat, breath and sleep.According to evolutionary school of thought we are hard-wired for sex which promotes survival of our species. This is true for other species also.