Romeo's love is unrequited for at least three reasons. The first is what we're told at the outset of the play: The houses of Montague and Capulet have an "ancient grudge.../ Where civil blood makes civil hands unclean," meaning that their families have been feuding for years. Romeo is a Montague and Juliet is a Capulet, so they aren't supposed to even meet.
But they do...and instantly fall in love. Knowing they are forbidden to see one another but being madly in love (and throwing caution to the winds, like the young teenagers they are), they are married in secret. Before they can break the news to their families, though, Tybalt (of the Capulet house) tries to pick a fight with Romeo, who refuses; Mercutio (Romeo's friend) fights him instead, and when Romeo steps between them to stop the brawl, Tybalt reaches under his arm and stabs Mercutio, killing him. Romeo, enraged, avenges Mercutio by killing Tybalt in a fair duel.
This naturally creates even more enmity between the houses. The anger and hatred is fresh. But worse: the Prince of Verona has forbidden the families to fight and promised that anyone who breaks the law will be banished. Thus, Romeo is banished...making it difficult for him to see Juliet.
Their love is finally unrequited when Juliet's plan to play dead so she can be moved to the family tomb backfires (when Romeo doesn't get the letter telling him that she isn't actually dead) and he hears about her death through gossip. He goes to her tomb and commits suicide, which makes any reconciliation impossible.