Applications in the biomedical sector have a rising demand for computational power due to the growing amount of biological data. However, the setup and maintenance of a sufficient computational infrastructure is costly. Cloud computing allows distributed computing over a network and maximizes the effectiveness of the shared resources. Nevertheless, security concerns rise when valuable research data is transferred to a public Cloud. Herein, we describe -- from the application and security perspective -- three biomedical case studies from different domains: Patent annotation, cancer outcome prediction, and drug target prediction. We elaborate on different strategies to secure the data and results in the Cloud as well as on the infrastructure needed. The proposed Cloud solutions could help to adapt other similar algorithms from different domains to benefit from Cloud computing.