Cloud Computing represents both a technology for using computing infrastructures in a more efficient way, and a business model for selling computing resources and services. On the other hand, such complex and distributed architectures become an attractive target for intruders. Cyber-attacks represent a serious danger, which can compromise the quality of service delivered to the customers. In this paper, we investigate the key research topics for supporting distributed intrusion detection in Cloud environments. Moreover, we present a distributed architecture for providing intrusion detection in Cloud Computing, which enables Cloud providers to offer security solutions as a service. It is a hierarchical and multi-layer architecture designed to collect information in the Cloud environment, using multiple distributed security components, which can be used to perform complex event correlation analysis.