EDIT: disregard the below bug report - logging off and logging back on after Fiddler update resolved the issue. This was a Windows 10 issue; not Fiddler's fault.
The default behavior of WIndows programs is that the app window can be moved/positioned using the Win + Arrow keys. The feature was expanded between Windows 7 and WIndows 10. Most apps get this behavior for free on Windows, but whatever UI toolkit was used to build Fiddler doesn't seem to support these standard window management shortcuts. Windows 10 x64 v.1511 Build 10586.494
Windows Key + Shift + Arrow sometimes works to move Fiddler between monitors depending on where my focus in Fiddler is, which view I'm using, and how wide the monitor is vs how wide the Fiddler results are. E.g. in wide view, Win+Shift+Left or Right seems to work reliably.
Windows Key + [Left,Right,Up,or Down Arrow] does not work in any situation as far as I can tell.
I think these used to work in Windows 7. I'm not sure if this was a regression in Fiddler, or if Windows 10 changed.