There has been some discussions around what the total number of VMware vCenter Concurrent vSphere Client Connections is.
Currently there is no limit, but it is recommended to keep this at a total of 30. Anything over this total and performance issues may be experienced.
It also depends on how you use the vSphere Client. If you have fewer entities opened in the inventory tree, your vSphere Client puts less burden on the vCenter server therefore it may support more vSphere Client without noticeable performance downgrade. Why? Because for every opened managed entity like virtual machine, the vSphere Client asks vCenter to monitor its status using vSphere PropertyCollector API. The more to monitor, the more burden on the vCenter of course.
Thanks to Steve Jin (DoubleCloud.org) for providing the above information.
In 4.0 the Max was 30. They increased the max in 4.1 to 100.
http://www.vmware.com/pdf/vsphere4/r41/vsp_41_config_max.pdf specifies it.
This document http://www.vmware.com/files/pdf/techpaper/VMW-Whats-New-vSphere41-vCenter41.pdf mentions 120, but i believe it to be incorrect. I was always told the config max docs should be the right ones.