Many different types of love exist, and Shakespeare certainly incorporated most, if not all, types in Romeo and Juliet. Some types of love are erotic, or infatuation; genuine romantic love; love between friends; and love between family members, such as between father/mother and child, or between siblings or cousins. As we are limited to space and won't be able to discuss all of them, but below are a few ideas to help you get started.
Erotic love, or infatuation, is especially exemplified in the love shared between Romeo and Juliet. Since they fell in love at first sight, we can question whether their love is the kind of love that is strong and enduring or rather just a fleeting infatuation. An infatuation is an "all-absorbing passion" (Random House Dictionary). Even Friar Laurence questions the legitimacy of their love, especially Romeo's love for Juliet since he so fickle. As Friar Laurence expresses it, "Young men's love then lies / Not truly in their hearts, but in their eyes" (II.iii.68-69).
Aside from varieties of erotic and romantic love, Shakespeare even shows us examples of love between friends. Love between friends is especially exemplified in the strong friendship felt between Benvolio, Romeo, and Mercutio. Benvolio cares so much for his friend and cousin that he feels sad to see Romeo so brokenhearted in the very first scene, which we see when Romeo asks Benvolio if he is laughing at him, and Benvolio replies, "No, coz, I rather weep," meaning that Romeo's sorrow is making Benvolio want to cry for him (I.i182). We especially see how much Benvolio cares for Romeo when he tries to persuade Romeo to forget about Rosaline. In addition, we see just how much Romeo cares for Mercutio when the fact that Tybalt slays him incites Romeo to such uncontrolled feelings of rage that he wants revenge for Mercutio's death.