Technological advances have resulted in organisations digitalizing many parts of their operations. The threat landscape of cyber-attacks is rapidly changing and the potential impact of such attacks is uncertain, because there is a lack of effective metrics, tools and frameworks to understand and assess the harm organisations face from cyber-attacks. In this paper, we reflect on the literature on harm, and how it has been conceptualised in disciplines such as criminology and economics, and investigate how other notions such as risk and impact relate to harm. Based on an extensive literature survey and on reviewing news articles and databases reporting cyber-incidents, cybercrimes, hacks and other attacks, we identify various types of harm and create a taxonomy of cyber-harms encountered by organisations. This taxonomy comprises five broad themes: physical or digital harm; economic harm; psychological harm; reputational harm; and social and societal harm. In each of these themes we present several cyber-harms that can result from cyber-attacks. To provide initial indications about how these different types of harm are connected and how cyber-harm in general may propagate, this article also analyses and draws insight from four real-world case studies, involving Sony (2011 and 2014), JPMorgan and Ashley Madison. We conclude by arguing for the need for analytical tools for organisational cyber-harm, which can be based on a taxonomy such as the one we propose here. These would allow organisations to identify corporate assets, link these to different types of cyber-harm, measure those harms and, finally, consider the security controls needed for the treatment of harm.