A lot of people in the world, mostly Nigerian have a limited knowledge of the crime occurring in cyberspace, known as cybercrime. Cybercrime happens in the world of computer and the Internet. This kind of crime has a severe impact on our economy, lives and society, because our society is becoming an information society, full of information exchange that is happening in cyberspace. Our research work is aimed at knowing the level of awareness of individuals on the existing phenomenon in Nigeria, and their impacts on Nigerian economy. A survey was carried out with the aims of getting these results using questionnaire as an instrument, the responses were quantitatively analysed using some statistical techniques. The results show that cracking, software piracy, and pornography among others are prevalent crimes in Nigeria. While the impacts of these crimes on Nigerian economy cannot be over emphasized. Recommendations were proposed on how these crimes can be minimized if not totally eradicated.