I have been using VMware Player under Ubuntu Desktop 12.04 to run three VMs for a while now. The only issue I had was a memory allocation problem, which was not the fault of the VM environment. I initially tried with Oracle Virtualbox, but was unable to get it functioning correctly. This was using both the a
wget from Oracle site and downloaded through Ubuntu Software Manager.
This may have been a specific issue with my host, but should you have success here you can have a look at some comparisons between these applications from xmodulo.
I am currently using VMware Workstation on my Windows 7 laptop without incident, although I only have four VMs and have yet to do extensive testing.
I would suggest this is a stable product to run under the conditions I outlined. VMware are even nice enough to provide a nice breakdown of the process for getting this up and running. You can find it here.