Decades ago during my college years I did something like this. I'd heard somewhere that taping plastic sheets (like saran wrap) to the window would help, so I did. But I don't think I did a very good job, it wasn't a tight seal that completely closed off the window. Today there are some modern products that supposedly do a better job. (see: window insulation film)
Some companies (like energy-film.com) make plastic that goes directly on the glass. Obviously that won't create an air gap, which is a key part of the insulation strategy. The energy-film.com website explains they've embedded nanoparticles in the plastic that selectively allow visible light through while blocking infrared light. While that will block light transmission, does it actually improve the R factor of the window? They don't make any such claims. Further, an article on chiefengineer.com (What Most Window Film Manufacturers Won't Tell You - And Why) dismisses this sort of product to use in stopping heat loss. That article says films applied to glass are great at stopping heat gain during summer, but not so good at stopping heat loss during winter.
VIDEO: How to Weatherize Windows with Plastic Film Insulation- DIY Home Improvement - Shows how to install a modern version of what I'd done 30 years ago with saran wrap. It looks pretty painless. VIDEO: The Fix Its - Shrink Wrap Your Windows for Winter shows installation of a similar kit, but for exterior use.
The technique shown is for one season only.. The plastic sheet is shown completely blocking the window. So when summer returns in a few months, won't you want to open that window again? To do so you'd have to completely remove the plastic.
Surely there's some kind of plastic which installs on the window, rather than the window frame?
VIDEO: bubble wrap window insulation - Instead of simple plastic sheets, this video shows use of bubble wrap. The bubble wrap sections are cut to the size of the glass pane and glued to the glass. They're easily removable and can be saved away and reattached next year. I like this idea quite a bit. The video also shows the kind of windows that are in my house.
Obviously bubble wrap interferes with being able to see out the window. Use appropriately.
The video also shows a different method of installing simple plastic sheets. Instead of taping the plastic to a window frame, the plastic is taped to a wooden frame that's then wedged into the window frame.
That video refers to: A very rough go at measuring the actual heat loss performance of the bubble wrap - Which is, as the title says, a very rough estimate at measuring bubble wrap effectiveness in stopping heat loss. The results are promising.
VIDEO: How to install Advanced Energy Green Window Panels - Shows installation of a product which is an add-on frame that is similar to the wooden frame shown in the bubble wrap video above. The design is very ingenious, and the video goes into lots of details on the design, sizing the panels, installation and removal. The design shown can be easily removed or re-installed.
VIDEO: Seal & Insulate: Windows & Doors - Shows an excellent overview of simple tips to improving the insulation around windows, doors and even electrical outlets (using electrical outlet insulation gaskets).
VIDEO: How to Caulk Windows For Dummies - Shows how to use a caulking gun. While putting plastic on your windows, might as well seal up cracks. Caulk is one way to do so.
VIDEO: How to Insulate and Seal a Rim Joist- DIY Weatherization for Your Home - also goes into insulating other things besides windows, in this case the joists in your basement.
Measuring home heat loss through windows or pipes with a hand-held IR thermometer - Make sure that adding plastic to the windows actually helps.