Odysseus' wife, Penelope, has suitors for a few reasons. First, she is a beautiful woman, and from the beginning of time, women who are physically attractive have had admirers. Second, her husband has been gone a long time...so long, in fact, that most people believe him to be dead. In this case, she is free to marry once again should she choose to do so. However, we know that Penelope is stalling by creating new challenges for the suitors to complete because she secretly believes that her husband is alive and will return home to her. Third, Odysseus and his wife are wealthy people. The new husband would gain much wealth in addition to the lovely new wife by marrying her.