I think this has been answered but there are two possible answers:
1. You VMFS datastore is full: Then all vm's on that datastore will be suspended until you free up some storage. This can be caused by snapshots, thin provision growth, bad placement, powering on virtual machines etc. The simple answer is you have to move virtual machines off the lun before vm's can be powered up.
2. You guest VM hard drive fills up: Depends on operating system but most will keep running but be unable to write logs etc... until you clean up space. It's really dependant on the OS. There is no difference here from a physical machine. If a Physical OS will shutdown when out of storage the virtual will too.
Thanks,