Healthcare Information Systems are nowadays among the world's largest, fastest-growing and most information intensive industries. Additionally, Intensive Care Units are widely considered as the most technologically advanced environments within a hospital. In such environments, physicians are confronted with the challenge of storing and analyzing terabytes of data that stream in real-time from inpatients to centralized clinical information systems. In this paper we present the system architecture and early experiences from ICGrid (Intensive Care Grid), a novel system framework that enables the seamless integration, correlation and retrieval of clinically interesting episodes across Intensive Care Units, by utilizing the EGEE infrastructure. ICGrid is based on a hybrid architecture that combines i) a heterogeneous set of monitors that sense the inpatients and ii) Grid technology that enables the storage, processing and information sharing task between Intensive Care Units. ICGrid makes it feasible for doctors to utilize the EGEE Infrastructure through simple, intuitive user interfaces, while the infrastructure itself handles the complex task of information replication, fault tolerance and sharing.