To eliminate the frustrating "browser isn't compatible" error when attempting to run the vSphere Web Client in IE11, enable Enterprise Mode for the site you are launching the client from.
Enterprise Mode causes the browser to present a legacy User Agent String and to enable some deprecated capabilities. This can be done on a page-by-page basis using the Site List feature.
To enable Enterprise Mode w/Site Lists:
First
Create an XML file containing the URLs of your vSphere WebClient launch points and post it in a centrally accessable location. Here's a copy of ours.
We use a central server to launch the vSphere Web Client and to host the vCenter Converter. Its fqdn would replace xxxx.xxxx.xxxx.com.
If you have multiple servers hosting the web client you'll need to add a <domain> section for each one. Don't forget to include the <path exclude="false">/vsphere-client/</path>. It won't work without it.
SiteList.xml
==========
<rules version="5">
<emie>
<domain exclude="false">xxxx.xxxx.xxxx.com <path exclude="false">/vsphere-client/</path></domain>
</emie>
</rules>
Second
Add the following values to the EnterpriseMode registry key on all workstations using IE11 to run the vSphere Web Client:
[HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Internet Explorer\Main\EnterpriseMode]
Enable=""
SiteList=file://<path to shared xml file>/SiteList.xml
Close all instances of IE running on the workstation. The next time you browse to the vSphere Web Client you will no longer see the "browser incompatible..." warning when it launches
NOTE: Enterprise Mode is installed as a part of Win7/WinServer2008R2 Update for April 2014 (2929437). Check that this update is installed before using this procedure.
Enjoy!
Robert