Virtual Cluster?

I’ve been doing research in virtualization, and most of the articles are about consolidating multiple virtual servers into one physical server. My goal is just the opposite: I want to run one virtual server within two physical servers for high availability and possibly load balancing.

I’d like to use a single embedded hypervisor so this is not running on top of a full-blown (bloated) server OS. Shared storage is probably a necessity here.

Is this possible? Recommended? What products are out there for this? Any feedback is appreciated. Thanks.