Song lyrics usually rhyme, but they don't have to. Establishing a pattern of rhyming and then breaking it is one way to give structure to your song. For example, the leadup to the chorus is one place where rhyme schemes often lapse.
Some songs don't rhyme at all, and no one seems to miss it. If you find your song getting bogged down in a struggle to rhyme, try skipping the rhymes. Maybe you're working on a song that doesn't need it.