Some males wake up with an erection and some don't. Either way, both are completely normal. Studies have shown that men have several erections and arousal periods while in the dreaming phase of sleep called Rapid Eye Movement (REM). Women also experience an arousal response, but it is not marked as easily as an erection is. Also, males are known to have wet dreams (ejaculate) in their sleep and females are known to experience orgasms. Why this happens in males and females is unknown. People used to think it was because of a full bladder, but resent research discounts that notion.