I have used iframes from varying sources and never had an iframe stipped out of a post or page. Your theme or a plugin is most likely causing this.
Does it happen with default theme and all plugins deactivated?
I can answer that as a NO, as I use WP3.8 and default themes in multiple sites, again, no issues with this.
So test as noted and discover which is causing the issue.
Additionally, you could disable the Visual Editor. Code is stripped in the Visual Editor, so either disabling the Visual Editor or simply always staying in the HTML Editor (Do not switch to Visual Editor) will allow that your HTML is not stipped.
Above assumes when you paste the video embed code in your post or page that you are doing so in the HTML Editor. Do not do so in the Visual Editor.