Cloud computing holds the possibility to annihilate the needs for setting up of costly computing infrastructure for IT-based services and proffering IT Solutions. It offers an adaptable IT architecture which is accessible via the internet for lightweight and hand-held compact gadgets. The concept has encouraged numerous folds to improve in the capacity or capabilities of the existing and new software. In the cloud computing environment, the whole data/information is available over a set of networked resources, empowering the information to be accessible via virtual machines. Considering the fact that the cloud computing server may be located in any part of the world beyond the reach and control of users, there are various security issues and privacy challenges that need to be clearly understood with a view to identifying how to mitigate them. Likewise, there are possibilities of the imminent breakdown of servers which have been witnessed in recent times. This research addresses the security issues connected with cloud computing, provides analysis of the militating factors against the successful implementation of cloud computing and proffers useful recommendations on how to ameliorate identified issues.