These newspaper articles claim that bubble wrap is an effective window insulator:
Cheap and effective: using bubble wrap on the inside of your windows will help reduce energy bills
As homeowner Denise Wheoki has discovered, the cheap plastic wrap traps heat.
Save money on heating bills during winter
Make your house warmer by sticking sheets of bubble wrap over windows and sliding doors.
You can use bubble wrap to insulate older windows or windows that are not commonly used around the house. Simply cut the bubble wrap to shape of the window, spray the glass with plain water, and attach. The sunlight can still come through the window, creating radiant heat, but the bubble wrap traps it inside to prevent leaking. The bubble wrap is said to increase a window's efficiency rating from an R-1 to an R-2, essentially changing a single-pane glass one into a double-pane one.
An ecorenovator forum user posted an anecdote of having success.
The This Is Money describes a related idea of using cling film stretched across the frame to reduce drafts.
Are there any studies to show the effect on energy use?