Make sure you have UAC disabled and running IE as administrator:
http://world.episerver.com/FAQ/Items/Installing-ActiveX-Controls-in-EPiServer-Client-Components-on-Windows-Vista/
Inspiration links:
http://world.episerver.com/Forum/Developer-forum/EPiServer-CMS-6-CTP-2/Thread-Container/2011/8/Problem-with-Advanced-File-Upload—wont-work/
http://blog.fredrikhaglund.se/blog/2008/07/22/installation-of-episerver-components/
Solution:
Go to this folder:
C:\Program Files (x86)\EPiServer\CMS\6.1.379.0\Application\UI\CMS\ActiveX
Open the EPiServerClientComponents.CAB file and extract the contents.
Run a cmd prompt as administrator and enter:
cd “C:\Program Files (x86)\EPiServer\CMS\6.1.379.0\Application\UI\CMS\ActiveX”
– or wherever you extracted the files
regsvr32.exe EPiFileUpload.dll (install fileupload)
regsvr32.exe EPiOfficeIntegration.dll (install office integration)