By default, iTunes will behave just like any other application on Mac or Windows PCs, and stay in the background when you launch or maximize another program. As you may know from an earlier tutorial, the iTunes Mini Player can optionally float above other application windows, a very practical feature that allows you to switch between audio tracks without having bring the iTunes window back to the foreground. But you can also force iTunes to stay above other windows, and "float" over them, while a movie or TV show is currently playing, and this tutorial explains how to enable or disable this setting.
Once you are inside iTunes, click on the Edit menu and choose "Preferences" (this is on Windows, like the Ctrl+comma keyboard shortcut - on a Mac, click on the "iTunes" menu, and choose "Preferences" or press Command+comma).
Note that this setting also affects your personal video files and video podcasts - basically anything that would play in the "movie player" popup window, except for music videos, whose behavior is controlled by another dropdown menu, right before the one you re-configured. If you experience intermittent or permanent problems with this feature, please read on:
If you have spent any time in Apple's support forum, you'll know by now that this feature has stopped and resumed working throughout the years, and the problem (especially once reported by you or other iTunes users), tends to be fixed in the next round of upgrades delivered through Apple Update. Nonetheless, here's a half-baked solution you can use as alternative until Apple addresses the issue.
On a Mac, just resize both iTunes and the active window to make them share screen real estate as needed.
On Windows, the same workaround will do as well; but on Windows 7, you can also use "Aero Snap" to quickly force two separate windows to share the screen in a vertical or horizontal split by dragging an opened application towards a side of the screen, and releasing when you get a visual cue that the snap and resize is about to take place. In the case of making iTunes share a portion of the screen, this will work best if you are using a high enough screen resolution to accommodate all interface elements on your main application, while leaving enough room for iTunes and the video playback (how to change screen resolution in Windows 7).