For the most part, Romeo and Juliet are star-crossed lovers simply because we are told in the introduction that they are. Shakespeare lays out the entire situation for us in the beginning and even tells us that the outcome will be tragic. We can see evidence that they are star-crossed throughout the play. First, their families hate each other. They have parents who do not support their union. They have to run away to get married, and when they manage to do so, they end up dying tragic deaths. In the end, the only way for them to be together is through death- there is no happy ending for them. Thus, they are star-crossed and there would not have been anything either of them could have done to change the situation because this was laid out for them from the beginning.
Star crossed means ill fated. It means that Romeo and Juliet were destined to be separated and unable to be together. Romeo ends up at the party where he meets Juliet by happenstance. He wasn't supposed to be at the house of his enemy, but an illiterate servant changed the course of his evening. Romeo and Juliet meet, unaware of who the other truly is. They become attached to each other before the realize their families are feuding. From the beginning, they have trouble sneaking around to see each other. They marry in secret and Juliet is immediately promised to another. Nothing seems to go right for the young couple. Perhaps Juliet could have left Verona and lived happily ever after with Romeo in Mantua, but in her desperation she agrees to a wild plan. The plan falls apart when Romeo isn't told of the details. Everything that happens between them goes awry.
They are star crossed lovers because fate seems to conspire against them. They meet and fall in love (which is itself sort of a bad thing given their family backgrounds) but then things go badly for them. Things happen like Romeo having to kill Tybalt. Friar Lawrence concocts this plan, but they misunderstand what is going on. It seems like they simply don't have any good luck at all.