Cloud computing is set of resources and services offered through the Internet. Cloud services are delivered from data centers located throughout the world. Cloud computing facilitates its consumers by providing virtual resources via internet. The biggest challenge in cloud computing is the security and privacy problems caused by its multi-tenancy nature and the outsourcing of infrastructure, sensitive data and critical applications. Enterprises are rapidly adopting cloud services for their businesses, measures need to be developed so that organizations can be assured of security in their businesses and can choose a suitable vendor for their computing needs. Cloud computing depends on the internet as a medium for users to access the required services at any time on pay-per-use pattern. However this technology is still in its initial stages of development, as it suffers from threats and vulnerabilities that prevent the users from trusting it. Various malicious activitiesfrom illegal users have threatened this technology such as data misuse, inflexible access control and limited monitoring. The occurrence of these threats may result into damaging or illegal access of critical and confidential data of users. In this paper we identify the most vulnerable security threats/attacks in cloud computing, which will enable both end users and vendors to know a bout the k ey security threats associated with cloud computing and propose relevant solution directives to strengthen security in the Cloud environment. We also propose secure cloud architecture for organizations to strengthen the security.