Cupid is a powerful part of Shakespeare's stories. In A Midsummer Night's Dream, for instance, Oberon sends Puck to a place where Cupid's arrow fell to the earth onto a flower that holds such a powerful spell, that it can make someone fall in love with the first person--or thing--she/he sees upon waking, even a man with the head of a donkey. While the Elizabethan audience would not necessarily have been been so drawn to other gods or demigods from mythology (though they would know them), Cupid falls right in there with fairies, sprites, changelings and witches, which Elizabethans believed in completely. They believed that if someone ventured into the forest after dark, that person was at the mercy of fairies who weren't necessarily harmful, but loved to play tricks on humans. However, where witches were evil, and fairies were playful and mischievous, Cupid was the entity that controlled love: a powerful force if one believed. I can only imagine that as love is believed to be a powerful force today, and for hundreds of years volumes of poetry have been written about love—lost, found or somewhere in between—Cupid was at one time a necessary ingredient for love to thrive. For if Cupid were present, who could resist his "magic?"
Act One holds the conversation between Benvolio and Romeo. Rosaline will not give in to Cupid's spell, but is smart and wise like Diana, the huntress. Roseline will not succumb to Cupid's power, or man's wooing. Cupid is, as others have said, the epitome of love, but some people (such as Rosaline) cannot be conquered by Cupid, by love.
Cupid may be generally seen as "Doctor Love," but whenever love is not the result of Cupid's involvement, it must come from the direction of the plot development. Cupid—in Romeo and Juliet—is presented as Shakespeare intends the character to affect the story's outcome, so Cupid's characteristics are limited only to the writer's imagination.