Do you need to have an application window sit on top of other windows? For example, you can keep a calculator handy at all times. Regardless of what other window you switch to, this window will always be visible.
Some Windows applications, such as Task Manager, include such functionality, but most do not. For apps that do not, an app appropriately named Window on Top can help.
The app runs in the background in the tray/notification area. It consists of one single window.

Window on Top
To make any window stay on top of everything else, either drag the hand shown in Window on Top onto the application window or use the shortcut key Ctrl + F8 while the desired application window is active. Repeat to cancel.

The Notepad window remains on top even though I'm typing in Firefox
An alternative to Window on Top is PowerMenu. PowerMenu allows you to keep any window on top through right clicking the title bar or taskbar item (pre-Windows 7 only). It also includes features such as window transparency.

PowerMenu in Context Menu
However, I found that the menu does not work if the window does not use a standard Windows title bar (or has no title bar), such as Firefox and Chrome.
Have a different app to keep windows on top? Share with us in the comments.