WinBeta got access to a pre-release version of Cortana running on Windows 10 in desktop mode.
The site notes Cortana can do pretty much everything the Windows Phone version but be aware that the user interface of this preview is very crude, the final product will look much better.
From the get go, Cortana can do pretty much everything the Windows Phone version can. This includes reminders, call people with skype, check my location/maps, play/pause music, launch apps, check the weather and more. Right now, Cortana doesn't have a personality in Windows 10, meaning she doesn't answer questions like "Who are you", however we have it on good authority that she will have this ability by the time she rolls out to the public.