In the last few years, research has been motivated to provide a categorization and classification of security concerns accompanying the growing adaptation of Infrastructure as a Service (IaaS) clouds. Studies have been motivated by the risks, threats and vulnerabilities imposed by the components within the environment and have provided general classifications of related attacks, as well as the respective detection and mitigation mechanisms. Virtual Machine Introspection (VMI) has been proven to be an effective tool for malware detection and analysis in virtualized environments. In this paper, we classify attacks in IaaS cloud that can be investigated using VMI-based mechanisms. This infers a special focus on attacks that directly involve Virtual Machines (VMs) deployed in an IaaS cloud. Our classification methodology takes into consideration the source, target, and direction of the attacks. As each actor in a cloud environment can be both source and target of attacks, the classification provides any cloud actor the necessary knowledge of the different attacks by which it can threaten or be threatened, and consequently deploy adapted VMI-based monitoring architectures. To highlight the relevance of attacks, we provide a statistical analysis of the reported vulnerabilities exploited by the classified attacks and their financial impact on actual business processes.