We're moving to a Hyper-V cluster with data center licensing soon, and will be able to spin up several virtual servers if needed. We have about eight applications which use SQL databases. Is there any advantage/disadvantage to setting up a separate SQL server for each application, versus keeping everything running on one large SQL server?
The fact that this is on HyperV is mostly a red herring in this situation. Approach it with the same criteria you would use for placing different SQL databases on same or different instances on actual hardware.
Per your comment : if you're doing it with all on one instance now and not having problems, keep doing that, on a correctly-sized VM. Adding more VMs will just use more resources for additional OS instances. What sort of maintenance would you be doing on one database that is impacting other databases? Unless you're doing something like re-indexing in one database that is impacting performance in other systems, and they don't have overlapping maintenance windows or periods of allowed reduced performance. This is what I was getting at by saying the only real reason to do this is for performance reasons. Otherwise, try to consolidate.