I have a Nokia 635 and want to know what version the stock IE browser is. Is there some way to tell on the device?
Lumia 635 comes with IE 11,you can check the version by going to internet explorer->settings->about.
Windows Phone 8.1 comes with Internet Explorer 11 Update (which has some additional changes over the desktop version).
For completeness, Windows 10 Mobile comes with Edge, whilst Windows Phone 8.0 came with Internet Explorer 10
Go here from that browser: http://www.whatsmybrowser.org
This is not technically on your device, but it'll still tell you on your device (as long as there's an internet connection).